Will enterprise pick me up from my hotel?

Usually they do. But for the center that serve airport, you may have to call and check with them or you can go to airport using the hotel shuttle and then take enterprise shuttle... if time permits. Enterprise is good in general.

I am not sure. They run a free shuttle bus from Los Angeles airport

Several times I had different requests from Enterprise but I haven't asked that kind of request. But mostly especially Enterprise is one of the best solution maker in between car rental companies. Try it and lets learn together.

Depends. You gotta give them enough notice. Call and ask the location.