I want to cap the existing bathroom rough-in in my basement and put in a bathroom at a different location. I have drawn up what I have in black and what I want to do in red. The drawing is not to scale. I have a few questions:

1. I can't find a vent anywhere in the ceiling over the existing rough-in so I think the were probably going to use an AAV (which is allowed in my area). After reading up on AAV's, I think I only need one for the new bathroom at the sink/lav and then the other two drains effectively wet-vent back to the sink and then dry vent from the AAV at that location. Is that correct?

2. No one else in my neighborhood has a backwater valve so I am not sure that is what the 4th pipe is, however a few plumbers have told me that is what they suspect it is (I would be happy to hear your guesses). Should I put a new one in? And if so, should it go between the existing stack and the new shower to protect the entire new bathroom?

3. Am I missing anything obvious? This doesn't seem too bad of a job (other than the jack hammering).

Thank you in advance for responding.
Matt