I believe they have camping, but it is not the type of camping you expect. Often in China, they do not allow open fires. Your best bet is to stay in a hotel. As for a tent, I am unsure what they allow. Sorry.

During the summer, the temperatures can be quite cool and the upper mountains still have snow. With the altitude, I suspect that there could be quite a bit of snow in that area.

You have to pay to enter the park -- Blue Moon Valley is well inside the park so there's no avoiding buying a ticket. Once you get in, you'll also have to pay the small fee for the shuttle bus to take you from the tourist center to Blue Moon Valley.

The buses are very frequent.

You can certainly buy an entrance ticket and walk around. We travelled by an organised day trip and I guess that is the best way of doing it unless you speak Chinese and want to get there independently.