The "Favorite" feature is borderline useless; the only real function it serves is to allow you to build a list of questions you might wish to refer back to later.
Given there's no particular reason why you wouldn't want to occasionally refer back to your own posts... And plenty of reasons why you might... It makes little sense to disable this.
Note that ...
Having a question marked as a favorite doesn't earn the asker any reputation, so that doesn't really matter.
If you upvote the answer you prefer every time you visit the page the arrow will be filled in, so you know that's the one you upvoted, poor man's favorite I guess.
Also if the answer is useful then clearly the question has merit, if the post is of ...
No it is not possible to favorite an answer in SE. You can only favorite a question.
Maybe you can change this to a feature request, though I doubt it'll be accepted or implemented in the near future.
Meanwhile however, you can bookmark or save a link to the answer you wish to favorite in your own browser.
There is no "bulk" way of removing favorites, but there is a way which is somewhat easy.
Go to your favorites page, and click on the favorite icon of each question one by one. At least you won't have to go into the question's page each time.
Strictly speaking, the text "This is a favorite question (click again to undo)" is perhaps unambiguous.
But depending on how one happens to read it, it may take considerable effort to see what it means, and some users may be confused or even fooled into thinking it means the opposite--as you say.
So I think you're right. This would best be changed. Your ...