What needs done to put a half-bathroom in this basement? (photos included)
It is hard to tell what is going on in the first pic. Is this a stack under other fixtures? Is it 3"? If so, you could tie new fixtures into it that would need to be vented elsewhere. I would figure out exactly what feeds that stack before doing anything with it though. If you already have 3 bathrooms feeding only that stack, it may be maxed out. If you tie into it, you will need to add another clean-out.
The second shows what looks to be a 3" pipe in the ground with a AAV-vented 2" pipe. The 3" is likely for a toilet. It is hard to tell if the 2" is a vent for it only or if it is a 2" stack that you could add a sink to. The fact that it has an AAV tells you there is no trap underneath, but doesn't tell you if it acts as a vent to the 3" line (connected via sanitary T at greater than 45 degrees to act as a vent) or if acts as an additional line (connected via wye). Since they are on the same floor, it may not matter and you could use it as a wet vent, but might have to check local codes.