Looking for a little help with my basement rough in (done when the house was built in 2001).

My main question is where the tub drain is intended to be. There is a mark on the wall that says "TUB", but no pipe. Is it buried in concrete, or should it be run above the slab over to the vent/drain pipe sticking out of the slab? If it is likely buried, any guesses on where it might be or how to find it (other than pounding away with a hammer)?

The toilet drain is sticking out of the slab, so that's no problem.

There is another marking for a lavatory on the wall, but no drain. I assume this drain should be run over to the vertical vent/drain pipe.

This vent is sufficient for all three drains, correct? Can it be run to the ceiling and connected to an existing 2" vent that is about 20 ft away? Or can I use a Studor vent?