New to the site, love the question and the forum.
Bear with me through the answer to what is being said, for what I hope will be a helpful answer to how it is intended to be applied.
To the question of whether Paul is being instructive or descriptive, this master-teacher really wants his audience to understand this concept, as their behavior indicates they are missing it. Thus, he is helping them understand how to recognize when they are living according to "the better way" (agapē) and when they are not. Still, while it is descriptive, the result is exclusive. If what they are living or experiencing does not fit the description, it may be some other form of love (see C.S. Lewis' "4 Loves"), but it is not agapē. Here Paul is just telling us what agapē looks like. It is somewhere else that agapē is given as an instruction.
To the question of what does it mean to "believe all things" Paul chose not to use another word (peithō), which tends to refer to an intellectual affirmation. Rather, he used pisteúō, which carries a sense of trust and expectation. Vine's states that it means "reliance upon, not merely credence." The word used usually refers to belief in God; but not always, as it is used to reference people who would lead astray (Matt. 24:26), the scriptures (Jn. 2:22), Moses (Jn 5:46,47), application of the law (Rom. 14:2), news of divisions (I Cor. 11:18), a lie (2 Thes. 2:11), and every spirit (1 Jn 4:1). So, while it is understandable why the author(s) of The Message inserted God's name in their translation ("...trusts God always.."), the author's intent is much broader. So what is it we should rely on? Here's the kicker, the answer is, "all." Mind you, as with each of the four "all things" referred to in 1 Cor. 13:7, Paul is very careful to use the anorthrous form of an adjective as a noun (all). With the definite article this would apply in totality (as in Matthew 8:32, when "... the whole heard of swine ... perished in the water."). With the way Paul uses the word in I Cor. 13:7, without the definite article, it refers instead to plurality ("as many"). If an umpire was officiating a baseball game in Greek he would use the definite article to tell the batter "That's all of them", meaning he has swung three times and is out; but, if the umpire was to use the same form of the word as Paul uses in 1 Cor. 13:7 he would be telling the batter, "Swing all you want." What Paul is saying is that agapē "relies and trusts anyone, anything, as often as."
So, now to the difficult answer to how we should apply this to the personal example given. The situation of an unfaithful spouse is truly a painful one. There is nothing trivial about living through that, and I don't know how else to convey that in a blog other than to simply state it up front. From a position stand point, there are a couple interesting thoughts to consider. First, the admonition to "...be perfect, just as your Father in heaven is perfect" (Matt. 5:48) is not a requirement of flawlessness, as the English would imply. It is, rather, an encouragement to mature. That is, to be better in your agapē today than you were yesterday, and to be more mature in this regard tomorrow than you are today. We are on a journey; hopefully one of growth and maturity in our love for God and others. This is why I Cor. 13 migrates to a discussion of "that which is perfect" and "when I was a child." See how the same word ("perfect") is used in Heb. 6:10-11 and 2 tim. 3:17, and I would encourage a study on how often it is used in the context of agapē.
As this site is committed to understanding the Christian position, another pertinent teaching to keep in mind is illustrated in Luke 7:36-50. There we see a woman of ill-repute weeping at Jesus' feet and wiping them with her hair. To those around, this discredited Jesus; for a holy man would not allow such an unholy person to touch him. But Jesus responded with a story about two men who both owed third man money, in differing amounts. Prompted by a question from Jesus, the Pharasee who was judging both Jesus and the woman responded correctly that the man who was forgiven the most debt would (in return) love the most. Jesus then explained, "Therefore I say to you, her sins, which are many, are forgiven, for she loved much. But to whom little is forgiven, the same loves little”. In that sense, we don't rejoice over sin; but, greater sin motivates the violated forgiver, as they know there is a direct correlation between the degree of violation and the degree of eventual reciprocating love. This is why the early Christians could rejoice in tribulation. They weren't psyching themselves up to act Christian, they really believed that living out agapē required their violation to produce repentance in others; and, the more that they would be violated the greater that likelihood would be. And, while being so violated, the believer's agapē was being perfected (matured).
Of course, as much as God's values are different from Man's, God's time table is different than ours also. So the conclusion/promise that "Love never fails" (I Cor. 13:8) begs the question of how we define "success" as much as it begs the question, "when do we make that determination." What we do know is that Jesus declared, "It is finished" (Jn 19:30) at what his mother, disciples and opponents probably viewed as the epitome of defeat - just as He died on the cross. Yet, we can see in hindsight that this was when he had fulfilled his obedience to The Father in the painful act of displaying His agapē to Mankind. To the difficult question of handling an unfaithful spouse, His example tells us that the journey will be hard, and that our focus must be on the end result, despite the shame (Heb. 12:2). The amazing correlation between vulnerability, shame and victory can be be further read about in Dr. Brené Brown's book (though not at all a religious book), "Daring Greatly."
This instruction to "believe all things" is absolutely pivotal to the gospel message. It is to say (as we demonstrate agapē toward God) I trust your word and your character to get me through this challenge. And it is to say to those around us (as we demonstrate agapē toward others) I know you hurt me today, but I believe you are better than that, and I will trust you for tomorrow. It is no wonder that this utterly unnatural virtue is compelling evidence of the very existence of God (John 17:20-ff), when lived out.
Regarding forgiveness, of course we are instructed to forgive as often as necessary; but, forgiveness does not necessitate foolish ignorance or complete susceptibility, no more than forgiving a debt necessitates making another loan. In that sense, as much as Paul is being descriptive, he is not saying, "Love is blind." Would it be truly loving to allow one's spouse to believe that perpetual infidelity is without profound life consequences? No, it would not. Therefore, love is not blind; for, as much as love sees what's going on, love also sees the heart of the beloved. They are just as vulnerable in the relationship; however, in that vulnerability, love does not attack; rather, it faithfully works to heal.