For planning purposes I am trying to figure out my plumbing under the slab. Can I safely assume that this is the right setup?
That should work if your wishful thinking is correct, though you might find it more practical to leave the stack alone and re-route the yellow vent around to where the red pipe is, rather than tearing up the stack to put the vent connection on the opposite side. Messing with the bottom of a stack is not trivial.
IF the pipes to the sink are big enough (and probably not if they were not intended for this) you could also route an above-the-slab dry vent from the sink and the sink drain line would wet-vent the rest, but if it's not big enough that won't fly.
Unclear from your comment, but if the place you &quot;need to move&quot; the yellow pipe is the upper floor, you can run it (properly sloped back to the drain) &quot;horizontal&quot; once it is 6&quot; above the flood level of the highest fixture in the floor it serves (the basement.) Not the highest fixture it serves, the highest fixture on the floor it serves. So you could make the move (if the upper floor is the area of concern) without getting into the concrete.