You can get water at Crystal Reservoir or Glen Cove on the way up. Not sure about the toll gate or the summit house, but if you call or email them (I can't post links due to new account) at coloradosprings.gov/pikes-peak-americas-mountain then they can tell you where to get water definitively. Also, this coming weekend (8/24 and 8/25) is the runner's marathon and I'd highly suggest scheduling for another weekend if you can.

edit: also, yes. It is paved all the way up on the toll road.