I will try to respond in a typical debate style: first I will respond to your specific points, and second I will present several responses in defense of marriage and against pre-marital sex (I'll use this as a blanket term for sex-outside marriage). I appreciate the order in which you provide your points, because I believe your conclusions about the first point will inform how you answer the two examples which follow.
Point 1: There is no explicit command to avoid pre-marital sex
Your first point comes from a university piece suggesting that, contrary to what seems 'common knowledge', there are not explicit commands against pre-marital sex in the Bible. Two responses:
R1. This is factually wrong. There are explicit commands in scripture that tell us that sex outside of marriage is sinful. 1 Corinthians 7:8-9 (NRSV) reads:
To the unmarried and the widows I say that it is well for them to remain unmarried as I am. But if they are not practicing self-control, they should marry. For it is better to marry than to be aflame with passion.
From this verse we can glean that (a) celibacy is 'preferable' for anyone seeking to serve God with their whole lives, but (b) sexual intercourse within marriage is acceptable and good, if it prevents sexual passions from causing them to seek sexual encounters (b) from which we can imply sex within marriage is good to prevent what is bad (sin) - sex outside of marriage. This third point is made even clearer when we read 1 Corinthians 7:36:
If anyone thinks that he is not behaving properly toward his fiancée, if his passions are strong, and so it has to be, let him marry as he wishes; it is no sin. Let them marry.
R2. The writer of this article misunderstands the purpose of avoiding sin. Reading Natalie Elliot's perspective we find that she has recently lost her belief that pre-marital sex is sinful, and although her basis for this revelation is supposedly the lack of explicit commands in scripture regarding sexual relations, we find at the bottom she desires to reject what scripture does say about sex! Regarding Paul's teaching in 1 Corinthians 6:18-20, she writes:
While it is undeniable that glorifying God through celibacy or through your body is a way to honor God, this verse is also getting at the submissive role of women at this time in the world.
We see her simultaneously recognizing that scripture is clear that sexual purity is important and nevertheless discounting the words of scripture because she sees it as dependent on a patriarchal culture. I'm not sure that she is whole-sale rejecting the authority of Paul's words in 1 Corinthians 6-7, and whether biblical teaching regarding women as cultural bound or not is a valuable question in and of itself. However, what is clear to me is that she uses a hermeneutical disagreement as sufficient grounds to not take a serious look at the universal character of Paul's teachings. She seems to assume he is combating "sexual exploitation" by recommending marriage, when his point is really much simpler. Sexual purity is a matter of obedience to God's purpose for humanity, specifically their use of the bodies that he created for them. Verses 9 and 37 of Chapter 7 make it clear that self-control is what Paul wants for the Corinthians. He desire they exhibit self-control because that is one of the fruits of the Spirit, who dwells within us to make us more like Christ not to bend what the Church has always believed and taught about what honors God to, as Elliot puts it our "unique needs" and "individual circumstances".
Point 2: Ruth's 'seduction' of Boaz demonstrates that pre-marital sex was sometimes acceptable. I'm not sure this exactly how you would phrase your point, but this is the conclusion your source seems to belief is supported by it. Three responses:
R1. Ruth is not 'seducing' Boaz but rather formally proposing marriage. So much of language is dependent on assumptions and body language. Where I currently live, it is common for men to walk down the streets holding hands, acceptable to sit next to other men with you hand on their knee or even thigh, and polite to kiss other men as a greeting. In NY where I grew up, these are all homo-sexually charged behaviors, but here, even same-sex attraction (let alone behavior) is strongly condemned and shameful. All that to say it's important to be careful when 'reading' the body language presented in biblical narratives.
Biblical Scholar Christopher R. Smith helps us to realize that in that context (a) laying near Boaz was "symbolically proposing marriage to him", (b) not seduction but "all of this is done honorably, within the customs of this culture", and (c) while 'uncovering' can have sexual connotations it is "disputed" that 'feet' are "ever" used even as a euphemism for sexual organs. In fact, unless you are already biased towards interpreting this passage strangely (i.e. if you are reading poetry, about a dream, or trying to prove a point), when reading the word 'feet' I think it is common sense to think the bible is referring to feet.
R2. If anything, this passage seems to imply that sex before marriage is not acceptable. If you are already inclined to think that pre-marital sex is acceptable, and that the incident between Ruth and Boaz shows that pre-marital sex is acceptable you are left with a difficult question: why didn't they have sex that night? I am unconvinced that even if she is uncovering his genitalia, and acting seductively, that she is then also having sexual relations with him. The text does not say they 'knew each other' here in chapter three, but it does say in 4:13 that after they were married "Then they came together, the LORD made her conceive, and she bore a son." And even if you argued that they had sex here, Boaz still sees it as necessary to immediately go get this marriage legal, suggesting that even if sometimes a man and woman have sex before marriage (there are several Old Testament laws about this) it does not validate the necessity that their relationship become a legal one.
R3. Be careful when drawing conclusions about what is and isn't sin from biblical narratives. This same point applies below to the David's encounter with Bathsheba. in P1.R2. I pointed to the hermeneutical rule regarding context to disagree with your source's interpretation. Now we turn to a second rule of interpretation: essentially, just because something is 'recorded' in the bible does not mean that it is endorsed by God. See this article:
Not all narratives are positive messages. Since the narratives reflect real life, the characters are not always heroes. Sometimes they demonstrate what we should not be or do. Sometimes even elements like prayers are negative models and represent how people should NOT approach God.
For example, scripture tells us that Solomon had many, many wives. This is not an endorsement of men today having many wives. Another example even seems runs counter to the conclusion your source hopes to draw from the Ruth and Boaz story. Abraham was married to Sarah. He had sexual relations with Sarah's servant (not his wife) and although God graciously blessed Hagar and Hagar's son, it turned out to be a negative experience for Abraham suggesting that having kids with your wife is a preferable practice.
Point 3: David and Bathsheba did not sin by having sexual relations. Point blank, wrong. Three responses:
R1. David sinned by sexually with Bathsheba and by killing Uriah. When a man in a position of power sees a woman naked, request she come to his palace, and ends up having sex with her, regardless of if she 'consented' or not, the power dynamics of the situation tell us that she was not in a real position to refuse. I won't go so far as to say David 'raped' Bathsheba since afterwards then ended up married, and and it appears not too unhappily so, but I will say that he abused his position to proposition sex from a married woman. When she was found to be pregnant, David tried first to cover up his action through deceit (suggesting he knew what he had done was sinful in the eyes of God and humanity) and secondly through second-hand murder. Anyone who reads 2 Samuel 11 and concludes David does not sin in this affair is not reading it honestly.
Of course the point made by your source is not that he didn't sin so much as he didn't commit adultery, your source writes:
...whatever his sin may have been concerning Bathsheba, did not commit adultery.
Perhaps then, we could suggest that David sinned, but his sin was murder, not adultery. This may be the author's interpretation based on Talmudic tradition, Nathan's condemnation of David's actions in 2 Samuel 11 make it clear that the sin God cares about isn't about the murder of Uriah, but the theft of what belonged to him, namely his wife. Nathan, speaking for God, seems to be pretty clear that David committed adultery.
Several conclusions may be drawn from this regarding pre-marital sex: (a) if David committed adultery then this incident has no bearing on pre-marital sex and certainly cannot be used to support it, (b) even if David did not commit adultery, this would only imply that sex outside of marriage is not acceptable - it is the fruit of illicit sex (the child) who dies which suggests that whatever went on (adultery or not) was unacceptable and sinful. When a child (Solomon) is later born within the confines of marriage, he is not killed but actually inherits the throne.
R2. Solomon was a questionably legitimate son. On this point I am a little less clear. Your source seems to be trying to acquit David of the sin of adultery because this would invalidate a later marriage between Bathsheba and David according to Jewish law. Three potential solutions: (a) The citation for Jewish law is not the Torah, so I unsure whether it was a standing statue in David's day and would dispel this whole problem. (b) As the the author does point out "David remained married to Bathsheba after the incident without reprimand, and because their son, Solomon, was allowed to rule and perpetuate the messianic line". Therefore, a skeptic might say, David already broke the law by killing Uriah and getting away with it, on a practical level, perhaps he simply gets away with marrying the woman he committed adultery with. Relevant to your main question their pre-marital sex was still sinful and punished as such but maybe God wasn't a stickler for the rules here. Or (c) God wanted sinners and anomalies in the messianic genealogy. Matthew 1 intentionally records several women, non-Jews in fact, and we may be forgetting that the line of Judah is continued not through his sons by marriage, but through his incestuous sex with a widow who he was not married to.
Perhaps we have gotten to wrapped up in knowing what is and isn't sin and we forget that God chose to become incarnate into human flesh, in a family line that included a lot of sinners. And yet he chooses to extend his grace to sinful humans, who often have illicit, sinful, and even adulterous sex.
R3. David is an example of exactly why sex outside of marriage is sinful. Whatever David's sin, it had huge negative consequences for him, Bathsheba, and their first child. He stands as a warning of what happens to relationships unprotected by the marriage covenant. 1 Thessalonians 4:3-8 reads:
For this is the will of God, your sanctification: that you abstain from fornication; that each one of you know how to control your own body in holiness and honor, not with lustful passion, like the Gentiles who do not know God; that no one wrong or exploit a brother or sister in this matter, because the Lord is an avenger in all these things, just as we have already told you beforehand and solemnly warned you. For God did not call us to impurity but in holiness. 8 Therefore whoever rejects this rejects not human authority but God, who also gives his Holy Spirit to you.
Whether pre-marital sex is sin, God hates sin, and he hates sexual immorality. Maybe you are still unconvinced by these arguments. I have mostly been responding to your arguments rather than making my own in favor of sex only within the confines of marriage but I hope this is what you are looking for in terms of counter-examples.
God made use to enjoy the use of our bodies, and that includes sex. That is why sex outside marriage (adultery, pre-marital sex, prostitution et.al.) is so easy a sin to commit, and that is why the Church is so vocal about condemning it. Adultery is a form of betrayal, and theft, which illustrates the wickedness of idolatry - of cheating on God. Pre-marital sex devalues the beauty of the commitment which a man and woman make when they become one flesh in being and act, as a metaphor for humanity's commitment to God. Think, being a Christian and taking communion before baptism - possible, yes, advised no. Sex outside marriage when can mean children growing up never knowing the stability of a family, and starts them on a cycle of broken relationships. Even if there are no children, it produces jealousy, shame, and all sorts of other things harmful to life. Finally, if it is dishonoring to God, it is sin.
Let marriage be held in honor by all, and let the marriage bed be kept undefiled; for God will judge fornicators and adulterers. Hebrews 13:4
The word fornicators typically included those having sex outside marriage - obvious from the fact that adultery is listed separately.
And if you are still uncertain, then for you it is sin.
But those who have doubts are condemned if they eat, because they do
not act from faith; for whatever does not proceed from faith is sin.
Of course the bible isn't a rule-book, and God is not merely a judge. Sex-outside of marriage is certainly sinful, But he is a gracious Lord who desires to forgive those who seek him in faith and repentance. He chooses sinners to be his children; adulterers and those who commit incest to be the people through who he came into the world to save us, sinners.