Yes. If you don't have onboard toilet, the want you to be close to the vault toilets. They have 10 ADA vault toilets.

Yes, you CAN Van Camp at all BLM sites, including La Posa South. There are numerous Pit Toilets scattered along the main road into la Posa South. There are also Pit Toilets at LTVA/La Posa North. LTVA/La Posa South also has a dumpster station, a Wastewater Dump station, and a Fresh Water Fill-up station.

Yes you can, but there are no facilities once you get away from the entrance area. You will need to be self contained or you will need to stay up close to the ranger stations and the restrooms, etc. Likely not what you really want to do since it's pretty dusty up there from the road and there will be lots of folks coming and going.