Is it possible to get an Uber or Lyft to pick you up at the Fort?

Yes my daughter did.

Yes I'm sure you can

I'm sure they get you fron the fort. Although it might be easier for them to find you from the visitor center. But I don't see a problem with either place.

Yes, there's a restaurant down there called grant house, very easy to ping. In the notes for Lyft put park across from grant house restaurant.

Probably