It's a wrapper over Google Play not F-Droid. Much nicer interface, you can filter for things like ads/paid/GSF, you can bypass some regional blocks, you can login with Google accounts or use it anonymously etc.
Never happened to me, but technically your account can get banned using Aurora since it's against the TOS. Also i mostly use aurora for privacy, so an different account only to download apps is a good idea. (Ideally you should even use the anonymous feature, but i had some stability problems with that so i switched to a throwaway account)
I use Aurora droid. It is much better than just Fdroid. Search works well, updates are easy, and what is that? App pictures and icons actually load?? 😂 It generally is nicer to use than F-droid and you can add many different repositories to it including custom ones