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.
