My question is about venting my basement bathroom group. The builder roughed in for a bathroom and it seems that the 2 inch pipe behind the toilet hole is the vent pipe. Can I simply connect this to the capped off 2 inch pipe the builder left with the label "air vent" written on it and would this vent all three fixtures (toilet, lav, tub) or do I need to vent the lav independently? This capped off pipe leads up through the main level and out the roof. Also, I need to vent the ejector pit and I am hoping to be able to vent it using this same vent line (the one that will connect to the currently capped off pipe). Is this possible. Sorry for all the questions, but finally, I'd like to add a small bar sink about 12 feet from the ejector pit. Can I run the drain line to the ejector pit and where should it tie into the ejector pit? Do I need to vent the bar sink, maybe a "cheater" vent as I noticed was talked about in another question? Thanks so much!

"Can I simply connect this to the capped off 2 inch pipe the builder left with the label "air vent" written on it and would this vent all three fixtures (toilet, lav, tub) or do I need to vent the lav independently?"
No, the lavatory will need its own vent. However, it may be revented back to the vent the builder left. Hpefully the tub will be connected to the lavatory drain and be wet vented by it.

" I need to vent the ejector pit and I am hoping to be able to vent it using this same vent line (the one that will connect to the currently capped off pipe). Is this possible?"
You may not use the house venting system for the ejector pit vent. The pit must have its own dedicated vent out the roof. The reasn for this is that the ejector pit vent exhausts air as well as pulling it in while the house venting are designed to pull air in. I realize this may sound like the house vent should work but that's the code.

I'd like to add a small bar sink about 12 feet from the ejector pit. Can I run the drain line to the ejector pit and where should it tie into the ejector pit? Do I need to vent the bar sink, maybe a "cheater" vent ?"
I would not tie directly into the pit. Tie into a line connected to the pit and vent the bar sink. You may either revent back to the other vents or install a cheater vent. Good luck, tom