This person did not give a complete e-mail address when asking the question. The only way I can provide that person an answer is posting it here.
1. What does the Bible mean when it promises that we will not be tested more than we are able? Why do we still sin then?
2. What does the Bible mean when it says that Jesus was subjected to all the temptations that we are going through. Specifically, was he tempted with homosexual sin as a heterosexual or as a homosexual? (Please don't just say that sexual sin is sexual sin...)
The first passage your questions referred to is 1 Corinthians 10:13. "There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it." I think the promise means just what it says, that God will provide a way out of every temptation. If he were not to do so, then he couldn't punish us for giving in.
You ask, then, why we still sin. We sin because we do not look for the way out, or don't use it. God provides the way of escape, but we may choose to ignore it. That is part of the free will God has given us. You could look at it like a man who is trying to commit suicide by drowning. Somebody may see him and throw him a lifeline or a floatation device. If he really wants to commit suicide he will push those ways of salvation away from him.
Your second question is about Hebrews 4:15. "For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin." You specifically ask about Jesus being tempted by homosexual sin. The verse doesn't say that Jesus faced every single temptation that people can face. After all, what is a temptation to one may not be to another. Those who know the meaning of the Greek say that the phrase "in all points" doesn't mean in every particular, but in every way. Thus he could be tempted sexually, perhaps, and that would be the same whether heterosexual or homosexual. To use your question as an example, there is a big difference between a man who has no desire to commit homosexual acts being tempted to do so and one who commits such acts being tempted in the same way. (By the biblical definition of a homosexual as one who has committed a homosexual act, Jesus could not be tempted with homosexual sin "as a homosexual." To do so he would have already had to have committed the sin. The concept of someone being a homosexual just because he has certain desires without acting on them is a modern invention.)
1 John 2:6 categorizes all sin as being one of three types: "the lust of the flesh, the lust of the eyes, and the pride of life." The account of the temptation of Jesus in the wilderness falls into these three categories, although Jesus was tempted more than just on that occasion. The point is, he could be tempted "in all points like as we" without facing every single temptation we do. He could be tempted in those three general areas, or in more specific areas without having to face specific sins, and still know what we face when we are tempted.