Mt. Huashan

I'm going to travel to Huashan in less than a week, but I am curious about leaving my luggage at the base of the mountain. Is it possible to check luggage for the night? I would like to arrive around 17:00 - 18:00 and check my bags. Then start to hike up the mountain until I can find a hotel close to East Peak. I would like to stay in one of the hotels on the mountain, but I am unsure how to book a reservation. Are the hotels on the mountain first come, first serve? After watching the morning sunrise I would like to go to the plank walk, and see the scenery in the daytime. I plan on taking the Gondola down around noon the next day.

So:
Is it possible to check luggage at the base of the mountain overnight?
Are the hotels on the mountain first come, first serve, or can I book a reservation somewhere?
What side of the mountain do I need to start on if I go at night? How do I get to this side of the mount from the bullet train rail station (I think it's Huashan North).