I can not answer the venting questions you have but would like to address the framing.
I see only two nails on the "Joist" or "Blocking" piece to the left of 'B' in your picture. Have the floor joists switch location here? If they are floor joist and not blocking do they bear down on that wall that I assume the vent runs through?
Remember no holes should be drilled through your floor joist within 2" top or bottom and the max hole size in most code books for a 2"x10" floor joist is 2 3/8". That joist has a few large knots in it and I would be adding another new 2"x10" to it before I drilled a new hole.