Yes there was a full size one in the cupboard. If you run out of shampoo etc just ask them, they have most things x
I'm almost sure there was. I don't use them but my gf does and I know she did not bring one on the trip. This hotel is one that will get things for you if you forgot anything. Very nice hotel and great staff.
Yes. Standard hotel quality hair dry, nothing special.
Get an answer from President Hotel Prague staff and past guests.