But there is one thing that I don't like - it's digging very deep in old posts in order just to ban someone. And now matter that user did that mistake only once, then changed his bejaviour and become good member of community.
Completely agree with this statement.
User made a mistake post one or few years ago. If this is the only mistake he/she obviously got familiar with rules and changed the behavior. Why ban if user is no longer making a mistakes or act against the rules in period like 1 year or longer. In this case delete the post and send user a warning you made mistake 1 year ago.
2nd plagiarism is forbidden but why are those post still on forum. If you ban the user because of that you should delete those post as well.