Plumbing – How big of access panel for DWV cleanout

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.

1. I believe that you are correct. Here is an article that discuss notching and drilling of studs: http://www.familyhandyman.com/walls/drilling-holes-notching-and-boring-holes-in-wood-studs/view-all

Load Bearing Walls:

Holes may not exceed 40 percent of the stud’s width (1-3/8 in. maximum in 2x4s; 2-1/4 in. maximum in 2x6s). The exception: Holes up to 60 percent of the stud’s width may be drilled through no more than two consecutive “doubled-up” studs.

While this article is not specific to BC, I believe that it is the same.

Note the limitation of only passing through two doubled-up studs. In you case, to get the new sink to about 2' over from the existing sanitary, you will have to pass through two studs. The first stud is already doubled-up but the second one is not and will need to be doubled-up. That will be as far as you can go.

2. Yes, can connect the drain of the bar sink into the vertical drain with the top portion acting as a vent for both sinks. The connection can be either above or below the existing as required to fit your new sink.

3. Most inspectors accept removable p-traps in lieu of cleanouts and is a common practice.