More or less this, though I'd avoid the +15% simply because whatever number gets chosen will just become a matter of debate. Instead, I'd make it so that there's a minimum amount of health (say, 20-25%), and if you win a round with less than that amount you get healed back to that point. But I agree that it's not really an important change.
I agree. The only reason I can think health regen would be useful would be if round 1 was very close then round 2 is normally pointlessly short, which is why I suggested having a minimum HP. But it's debatable if that's even a problem to begin with.