let's say I asked an interesting question which got a lot of attention and some really good answers. my problem was solved because of those answers and I've accepted one of them. but if I want to also pay some reward to the second best answer that already exists on my question, could I start a bounty for that sole reason? without misleading the site rules in anyway?

and does question needs to stay in featured area for 7 days?

If you’ve asked a good question, edited it with status and progress updates, and still are not receiving answers, you can draw attention to your question by placing a bounty on it

But I don't want to grab more attention on the question I just want to award an existing answer

I've no intension of doing it just now. maybe I'm not even eligible of giving bounties