The only one I did with a vent pipe was a huge one that went in a factory . I have never seen a vent pipe on anything domestic.
I am no sani expert but 1 1/4 to the sani , but I have always used 22mm copper from the sani to the soil pipe , would never risk plastic on that . Just use a strap on boss on to the soil pipe , biggest problem is the run to the soil pipe.
If the customer wants it , drum , and I mean drum it in to them that all that goes down the pan is what comes out of them , NOTHING else .
No wipes , No kitchen roll , No tampons etc etc etc