Rapiers are now a d8; basic melee attack is Strength mod + 1/2 level + proficiency bonus (If you are proficient with rapiers).
So that's Something + 1 + 3. If your strength mod is +1, you're doing fine. You do get to re-roll damage, though, since the damage changed on the rapier.
Mostly. Fighters aggro anything they hit; makes it harder for the target to attack anything else. With a d8, about 0.375, assuming you hit about half the time.
I think fighters may get some stances, but not at level 2.