Bigelow gave up their maintenance contract on their inflatable module attached to the space station when the contract expired in 2022. They said there wasn't enough money offered for them to continue.
They have built an
inflatable moonbase that is 330 cubic meters, not including the airlocks. The airlocks are double compartments. I think the airlocks will need to be more extensive than that if they want to keep all the lunar dust out of the
living/working area. The picture shows spacesuits hanging on the wall inside the living/working area. Those are probably emergency suits that are never used outside as it would be very hard to remove all the lunar dust from anything that goes outside.
Secondary launches after crafts reach Earth orbit.
The rocket to launch the station has two parts, the initial rocket to launch everything is built and working but the plans call for a second, upper section to make it possible for the station to be delivered to the moon. Basically it is a huge fuel tank that is used to provide fuel and energy once the initial supply of fuel is used up. There have been several existing and proposed designs but none have been tested in space yet. Several designs have been discontinued. It appears that the choice of fuel, probably for some kind of simple combustion rocket engine, hasn't been finalized yet. There are several proposed plans to make rocket fuel out of lunar surface materials.