F-Droid has a pretty strong foundation in my opinion. It just needs more resources to be able to publish app updates more quickly. It also needs a redesign, like you said, but I don't think there's a need to start from scratch
Yes, that would be nice, but at this point it would take a few billion to replicate all the functionality - who is going to be willing to pay for that and be still tied to Google? Might as well start a brand new smartphone/OS company...
So do you mean a store run by a company that has the money and intent to promote such a store enough for everybody knows about it, e.g. Facebook, Amazon, or Microsoft?
What else would you expect? Any other commercial app store - especially VC-backed - will eventually follow suit with Google's and Apple's stores in order to maximize profit over everything else. This includes denying any kinds of donation links.