laundry DWV question. Please help

Hi
I am putting in a new laundry drain. I have enclosed a couple pics--it is all just dry fitted. 2 questions.
first, I know that if I put a vent at A it will be right, but can I put it at B, or can it just be "wet-vented"--left as is? It is all 2 inch. (We are IPC here)

Second, I am planning on a sink where indicated--thats just a piece of pipe stuck there. Did I put things together right, or would I be better off running the p-trap directly off the stack?

Aslo--I took a picture of what I am replacing. The curly trap and standpipe are all 1 inch, I think--the drain barely fits in it, and the sink upstairs has overflowed up that pipe more than once when an unsuspecting person dared use the disposal while the washer was running. It looks like a nightmare to my uninformed eyes--and I know it acts like one.

thanks for all your help!

How are you going to vent the sink, where is the vent going?

so this thing comes up out of the floor, drains the sink (and now the laundry, makes a 45 degree bend, as you see, and just out of the picture, goes vertical and out the roof. That will be the vent. I think this pipe originally drained a basement sink and vents the kitchen sink upstairs. Does that help?

The vent for the washer needs to be within 5 feet of the trap.
The vent for the basement sink and the washer can be tied together, and extended through the roof.
If you don't go through the roof, you will need an AAV for it.

The upstairs sink waste on the left of your picture should have a vent going through the roof.

the vent does go thrugh the roof. OK. so the corner is only about 3 feet away from the trap. I will vent it at the corner, run the vent under the windows and tie it into the vent line to the left of the sink. Thanks!