I am currently banned from giving answers on Stack Overflow, and I want to know if there will be some kind of notification after the ban will get removed?
There is no kind of notification, since the ban will never be removed automatically after a certain period of time. There are two ways to get out of the ban:
- improve your existing posts; if they get enough upvotes, the ban will be lifted.
- regardless of the ban, you can make one new post every six months. Make it count, if it is well-received it'll help in lifting the ban.
No, the system checks when you try to post an answer (or a question if you're question banned). In any case you'll still be able to post once every six months, so if you do that make it a good one as that's an opportunity to get out of the ban if that post gets upvoted.
Best advice is to improve and undelete your old posts. Deleted posts can't garner any new votes so they do tend to weigh you down.