No. The wye is not in the wall. I think you are saying that you will feed the vent to the wye away from the wall. That implies your vent to the wye is horizontal. Not allowed.
Instead vent the tub trap at the wall with a vertical vent.
1. Yes.
2. No; if the lav were upstream of the toilet, then it could wet vent the toilet. It is not, at least as you diagrammed it.
Oddly, if you routed the 2-inch lavatory drainage through the wall over to the tub, that line could vent the tub and the toilet. Alternatively the lavatory drain could be under the floor, go behind the toilet, and join the shower drain line. It could be the only vent. If this routing seems odd to you, then you probably understand what I am describing. You should maintain 1/4 inch per foot slope minimum for your 2 inch.