Plumbing – How is a waste drain vent pipe vertical clearance measured

A shower drain needs a trap, so check under the cap on the left to see if there's a trap or a straight drain. If it's straight, then your assumptions are likely right that it's a toilet and the other one is a clean-out (fix that cap, you don't want sewer gases getting it). If you don't have a shower drain here, then I'm guessing it's only roughed in for a half bath.

I don't imagine the 2" would be anything other than a vanity drain.

With the "vent," I'm left wondering if it's really a drain since I see a clean-out installed on it. I'd recommend tracing that line up the walls, as best you can, to verify it really is a vent.

As for where the horizontal line is going to the left, perhaps a washer dryer, or perhaps the plumber screwed up the T and it should be pointing to the right for the sink. It's hard to tell from here.

I've found this:

Vent piping should never be less than half the diameter of the fixture drain it serves, and usually should be closer in size. For example, waste pipes of 3" and 4" diameters should be serviced by a minimum 2" vent pipe. And regardless of piping size, no vent should be smaller than 1 1/4" pipe. Dual vents which are to service more than one fixture should be slightly larger than required for a single fixture.

source: plumbing-basics.com