I'm only theorizing here. A network as big as verizon's is probably a hybrid network at this point since they've acquired many different cellular service providers using many different technologies (CDMA, PCS, maybe even GSM, etc). So it might vary depending on which cell tower you're currently using and what specific band / technology it is utilizing.
That's really just a wild-ass guess, though. Truth is, I don't know.
I think so. I don't use the stock app myself. You can always look at the settings and see. If it's there, then give it a shot.
I personally prefer the split option just because MMS messages take a bit longer and are subject to all that wacky network / wifi wonkiness that sometimes happens. Granted it is a LOT better on AOKP, but I still have the occasional MMS that won't send until I shut wifi off now and then.
Personally, I blame Verizon for insisting that MMS apps can't access their MMS servers over wifi. I understand they do it to make sure ppl who are sending mms messages are properly authenticated, but there are other and better ways of doing that which would be a lot less intrusive .. in my opinion anyway.