Matthew 39 and 40 then about divorce among Christian's

Verse 39 deals with matters of individual retaliation against those who have offended us in one way or another, but it does not mean criminal matters or military activities. The principle of non-retaliation is applied by Jesus in verse 39 against a person’s dignity, verse 40 against lawsuits to get one's personal property, verse 41 against a person’s liberty, and verse 42 which is against a persons property rights. 
"Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay saith the Lord" (Romans 12:19).
In verse 40 Jesus is saying to us not to argue over material things which will pass away anyway. If we will be generous to others then they will be generous to us.
Now your question about remarriage after divorce. If a man divorces and remarries he commits adultery (Luke 16:18). If a woman divorces and remarries she commits adultery (Mark 10:12). There is more to it than these 2 verses though.
"The Lord is merciful and gracious, slow to anger, and plenteous in mercy...For he knoweth our frame; He remembereth that we are dust" (Psalm 103:8, 14). "If we confess our sins, He is faithful and just to forgive us our sins" (1 John 1:9). This promise is specifically for Christians. It does include the sin of adultery if there is true repentance.  The Lord made this perfectly clear in dealing with the woman who was accused of adultery (John 8:4). Jesus reminded her accusers that they were not without sin. Those who had accused her all left. Then Jesus told the woman that He didn't condemn her then told her to go and sin no more (John 8:11). He didn't condone her sin but He did forgive her sin.

Principles

Stay true to your principles, to your values. Stick to your faith, and don't worry about the outcome. Just keep putting one foot in front of the other, meeting each day and everyone in it with Love, Kindness & Forgiveness. Do not let this world take your faith, hope or joy . . . DO NOT GIVE UP ON WHO GOD MADE YOU TO BE.

Pride

When pride comes, then comes disgrace, but with humility comes wisdom.
Why would pride bring disgrace?; what is it about pride that could do that? Isn’t a little pride a good thing; don’t they say that you should have pride in what you do?
Maybe that is it, right there: Have pride in what you do.
There is more than one kind of pride, just as there is more than one kind of love. We can be prideful, or we can be proud of the way we do things, and these are quite different. To be proud of our work means that we are pleased to do our work the right way; with quality and integrity. To be prideful on the other hand, is not so good, for in that case, we believe that we are better than other people, that we are more worthy, that we are more privileged, and all too often that the rules do not apply to us. An attitude like this leads a person to trouble.
This is the attitude that cuts corners, makes crooked deals and is willing to cheat others; why not if we are better than they are? This leads to disgrace sooner or later when we are found out.
Humility on the other hand, leads a person in a different direction, for a humble man or woman does not believe they are more worthy or superior to anyone else. They go about their business fairly, openly and with justice before God and Man, and that is wisdom itself.