Approx 80 miles. Uber would.

Yes

You can ask the the hotel staff if your going Mt.Fuji.Eithet,you can take a night bus or bullet train.If you have the JR railway pass,its much more convenient for you to travel.Also,the hotel can make arrangement for your trip.

Yes I've used it for videoconferencing several times

Yes there is 24 hour room service. There is also a Lawson convenience store opposite the hotel where you can get food and beverages

Savoy pizza in Azabujuban. Hands down