Dogs and campground availability

Anyone who camped in Great Basin :

Are there any problems having a dog? It looked like they can not be on the hiking trails. Is that correct?

And we will be there the 2nd week of August with a 17 ft trailer. Should we be able to get a campsite. The "first come, first served" policy makes me a little anxious.

How far ahead do we need to reserve the cave tour?

Thanks for whatever help you can provide.