Basement bathroom/wet bar using existing rough-in??

I have a bathroom rough-in in my unfinished walk-out basement as shown in the attached photo. I've also made note where my bathroom sink & wet bar sink would go.

- I assume the 2" line behind the toilet drain is the toilet vent. Should I dump my bathroom sink & wet bar sink drains into this 2" toilet vent, or do I need to run this over to my shower drain?

- Will the 2" toilet vent act as a vent for everything or do I need separate vent lines?

- I don't see a vent line available above this area... Although there is one set-up over the sump hole where my injector pump will go (which is about 20 ft away.) My bathroom area is next to an exterior wall. Do I need to try to tie in to the vent at the sump hole, or should I vent out the exterior wall, or?? If going to the "sump vent" how long can my horizontal run be when trying to tie in?

Thanks for any & all advice!

pipes

WE can only guess as to the layout of the piping, but connecting two sinks into that 2" vent riser may be more involved than just connecting one. You have to vent it through the roof, not the side wall, so if the pit's vent is installed properly, you can connect to that one.

Sorry for not being more specific... This is a top view... The "main line" shown is under concrete just below a 2x6 load-bearing wall (ie. framed but not finished.) The other pieces shown come 2' or so up out of the concrete and are capped off. The sump vent may be an option... But it will be a little awkward getting to it. (Attached photo shows general basement plan. Bright green rectangle would be bathroom wet wall. Bright green circle shows pit vent up under the stairs.) It seems odd that the builder wouldn't have left me an overhead vent "stub" closer to the bathroom fittings...