2)no, see below
3)no, unless downstream traps are vented. entire bathroom can vent on a 2" (tie the additional 1 1/2" vent into the 2" you propose)
4)yes, roll the wye's "up" so the leg of the wye is 45° or less from vertical, use the 45° elbow to roll the pipe back down to make it more horizontal
Adding an additional 1 1/2" vent for the tub would make your installation legal where I am.
Looks like you've been paying attention during your lurking. Not many can grasp wet venting a cellar coset through a lav. Good Luck.