What does the bible say about infidelity? When does God forgive you for your sins, if you ask forgiveness but you keep doing the same thing your not forgiven, right? What if you think what you are doing is right for you? What if somebody is on their way to righteousness but isn't there yet and they are killed, they aren't on the path of righteous but will they go to heaven?
In most translations of the Bible, marital infidelity is called adultery. There are many passages that condemn it. A couple should prove the point. In Galatians 5, adultery is listed as one of the works of the flesh (verse 19) as opposed to the fruit of the Spirit. Hebrews 13:4 says "Marriage is honourable in all, and the bed undefiled: but whoremongers and adulterers God will judge." Throughout the Old Testament the prophets compared Israel's going after idols instead of God as adultery or infidelity. Just as a husband can be unfaithful to his wife (or the other way around) so God's people can be unfaithful to him, although God will never be unfaithful to them. That should answer your first question.
It is not necessarily true that God doesn't forgive you even if you ask for forgiveness, if you sin again in the same way. See my answer on the limits (or lack of limits) to God's forgiveness at What Does the Bible Say About..Limits on Forgiveness.
You ask about doing what you think is right for you. By that standard there would be no morality, no law, no civilization. The Boston Strangler and Son of Sam (notorious serial killers of a previous generation) did what was right for them. Going farther back, Leopold and Loeb supposedly killed just to see if they could get away with it. If everybody did what they thought was right for them, regardless of what is right for others, we would be a society of thugs on the one hand, and fearful people on the other. There has to be a standard other than "what is right for me." God sets that standard; there is right and there is sin. Sin is wrong, even if you think it is right for you.
You talk about being on "the way to righteousness" and not being there yet. There is no being on a path to righteousness. We can't earn our salvation by becoming perfect; only Jesus was able to be perfect. We are either righteous in God's sight because we have been buried with Christ by immersion in water in order to walk in a new life (Romans 6), or we are unrighteous. We are righteous based on Jesus' righteousness or we are not. There is no in between. Once we have our sins forgiven, as long as we are striving to do our best to follow God, God forgives our sins. This is what John called walking "in the light" in 1 John 1:7. If we intentionally choose to walk in a way of unrighteousness, that is, to reject God, he will reject us.
Does that mean we will not sin. Certainly not! It doesn't even mean we won't commit the same sins over and over. There are some addictive sins, for instance, that are very hard to overcome and we may fall to the temptation many times as we try to overcome them. What God wants is our intent and our heart. Certainly, if we ask for forgiveness with no effort to stop sinning, then we are indicating that we are not a new creature, but the old man of sin. We must also repent, which means to be sorry for our actions and honestly intend to correct our way. God doesn't "sell indulgences;" he doesn't give forgiveness beforehand for something we choose to do against his will. He will, however, forgive if we admit we blew it and determine to do better in the future.