No, but they have taxis and uber services. Trip to places like the Monticello and the Vineyards, i.e. the Trump's, wine tasting, etc can be arrange with the concierge. The concierge are nice and willing to help to give information and directions.
No, there are taxis and Uber available.
I do not know as I drove there
Omni Charlottesville Hotel does not provide transportation from the airport to the hotel or viceverse.
Taxis are available for sure. I've seen people using Uber as well.
I don't know
Get an answer from Omni Charlottesville staff and past guests.