1 - Water is more expensive in relative terms but in absolute terms it's only a few hundred yen more. In the greater scheme of things (and costs to get there and back etc) it's something that is best just sucked up so you're not carrying extra weight for the sake of 5 bucks. Everything does get more expensive the higher you go so restock early

2 - If you're using the most common route (Yoshidaguchi trail from kawaguchiko 5th station) then yes, there are toilets on the descent about 2/3's of the way down. These are the best toilets you'll see on the trail (some can get pretty rank, think about that when you're buying water)

3 - Kind of up to you, it's big advantage is getting the full 360 degree view of the surounding countryside imo. You also need to think about how hard you'll kick yourself 3 weeks later when you start thinking "I should have done that" because it's not something you can easily get back to

4 - can't remember, I think we sent an sms but I'm not sure

5 - Not sure, I've not stayed in any of them

6 - bring proper wet weather gear, jacket and overpants (or whatever the outdoors hiking crowd call them). On one trip up we had perfect weather and we hardly needed any gear (not even a torch) and on another we were belted by a storm and weren't as well prepared as we should have been and it turned into a bit of a disaster. Freezing rain/sleet coming in at gale force with wet clothes is no fun. Likewise when you're climbing you stay quite warm but at the top waiting for sunrise it can get seriously cold (and windy). Make sure you've got layers and enough coverage to cope. Oh, and it's probably redundant but gloves are a must, not just to keep your hands warm but also to protect them.

Oh, and I'm not sure how many people go early in the season but be prepared for the fact that Fuji is probably the only mountain "climb" in the world where the hardest bit is standing in the queue

And have fun, the last time I climbed it was with a group of 4 friends out of season so there were probably only about 20 people heading up that night. We reached the summit first so for about 20 minutes or so we were alone up the top which was a pretty awesome experience.