No, answerers do not get notified about edits you make. The only people that get notified about edits are those who follow your question.
In general, there should be no need for such notifications. Note that you should not make edits "in response" to answers, in particular if these edits invalidate existing answers, see also this recent meta thread....
For a composite topic like quantum chaos it is recommended to use a tag combination: quantum-mechanics and chaos-theory.
Tip: To find questions about, say 'quantum chaos', it is often more reliable to search directly on keywords is:q quantum chaos rather than tags (as tags are not always applied).
No. While bounties technically allow transferral of reputation from one account to another, they are not meant to be used as gifts, and any bounty that is found to be used that way will be refunded.
The user will have to earn the necessary reputation points on their own. It's not that hard - 20 points are just 2 upvotes.
From the help center:
Questions can go through multiple close and reopen cycles, but each individual user may cast at most one close and one reopen vote per question.
A restriction like this makes it harder for a small group of persistent voters to override the community's intent on a controversial question, by persistently re-opening a bad question or ...