I'm going to try to give you a good answer to the exact questions you asked; then I am going to suggest a perspective for your consideration based on the issues you have raised in the comments you made surrounding your questions.
1) If you don't believe in the inerrancy of scripture, on what basis can you interpret scripture?
If you believe that scripture may contain errors, then it could contain errors at any point. There is really no passage that would be off limits. You would be forced to decide which scripture you think matches what God originally said, and which scripture you think got messed up somewhere along the line. You could do this a variety of ways, for instance you could examine the oldest documents. But ultimately you would have to decide which parts were pure.
2) Where do people draw the line when they talk about inerrancy?
Some groups say that the original writings were inspired and inerrant. If you google half a dozen denominations you will probably hit on this a few times. Unfortunately, no one has the original writings as penned by the apostles and prophets. So we are back to trying to figure out which readings are probably the closest match to the original writings based on the age or quality of the manuscripts and our skill in interpreting the languages into English.
Christian Missionary Alliance
First Baptist Atlanta: fba.org/main/statement-of-faith "without
error in its original manuscripts";
Westminster Confession section 1.8 OT Hebrew and NT Greek are to be
appealed to as a final resort
Other groups say that the concepts are inspired, but not the details. Since concepts are built up from details, again you must decide what is a concept and what is a detail, as well as which concept reflects accurately the ideas in the text.
Inerrant in what it intends to teach, not the details:
3) Is it without error between God's mouth and the original transcriptions?
Again, that is where many groups draw the line. And you are right to point out that it leaves room for problems down the line. And if we accept that premise, those problems are not resolvable without the original writings, which no longer exist.
If there are possibilities of error in the Biblical text, then you are right to point out that those errors could be generated by transcriptional mistakes or translation into our language. Errors could by exposed by science or history. Errors of interpretation could also be incorrect, but that would not affect the text itself.
However, let me propose another perspective for your consideration. Instead of asking "Where do people draw the line on inerrancy?"; I want to suggest a perspective on "Where does the Bible itself draw the line on inerrancy?" that I hope you will find interesting to consider.
"The words of the Lord are pure words: as silver tried in a furnace of
earth, purified seven times. Thou shalt keep them O Lord, thou shalt
preserve them from this generation for ever."
2 Timothy 3:16
"All scripture is given by inspiration of God, and is profitable for
doctrine, for reproof, for correction, for instruction in
This perspective would say that these passages point to God Himself preserving His words in written form on earth ("scripture") for the church to use forever. So by this point of view, at any time in history, the church has had access to His pure words in written form. Since we no longer have the originals, this view trusts that God has continued the preservation process including through the translation process so that people who believe Him and follow Him at least have the potential to access His pure words in written form.
This view depends on God to have a firm hand in the process. He has to guide translators that He chooses, and when they get it right, get that translation into the hands of believers and then bless their efforts so that those words get into the hands of everyone who needs them. All you have to worry about is whether or not you have the right version; but you don't have to really worry about that either because you can trust God, follow God, and seek after God and trust that He will put it into your hands and let you know you have it. "Seek and ye shall find" (Matthew 7:7), and "he will guide you into all truth" (John 16:13).
By this view then, you should treat the version you have as the pure words of God until God shows you it isn't and shows you to replace it with the one that is. If you have the pure words of God in front of you, and science or history disagrees with it, then either you are reading the text wrong or scientists and historians are interpreting their measurements and artifacts wrong. Not making wrong measurements, but interpreting what they measure the wrong way and using the puzzle pieces to construct the wrong picture.
God will make sure the recording and translating process results in an end product that has His pure words in the language or languages needed for that time in history so that believers are equipped. You can make errors of interpretation, but as you continue to read and study it you will realize those errors and the text will correct your understanding.
So rather than you finding and correcting errors in the text, the text will be finding and correcting errors in your mind.
This perspective is held by certain groups who would not draw the line as you have said but would put the whole process back on God to draw the line, preserve His words (Psalm 12), and put the right copies in the hands of believers as they need it.
Examples of groups who believe preservation by God through history:
group that holds to the divine preservation of all words:
group that holds to preservation in general but not to the detail
Your last question:
4) Doesn't the fact that we are constricted by the boundaries and limitations of language (whether spoken, written, or read) make inerrancy impossible?
Only if the process is up to us with no guaranteed oversight or intervention by the God who is not limited.