Normally the check valve has a fernco like connection of the ends. This can act as a union. You can use mission or fernco couplings with stainless steel wrapping to prevent pipe shifting.
The 2" vent should tie into the other vent systems, or make it's way through the roof. The 2" pumped discharge will go to the 4", and 4/10 hp is plenty.
The bathroom will be plumbed normally; traps and vents for fixtures before it ties into the basin. The toilet is it's own trap. I haven't seen a glue on adapter for a basin. Normally it's either a rubber inside seal, or a mission or fernco like connection.