Adding sink fixture to waste stack with existing sink fixture
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.


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