1) Two weeks is standard procedure; I see nothing wrong with that. If they don't have to train someone for your position, it's more than enough.
2) I'm surprised that the HR department didn't remind you that you have any sick or vacation time left! I would remind your supervisor that, indeed, you have this time left; which days does he/she think would be best taken.
It's been a LONG time since I've switched jobs, but when I gave notice, the pay for untaken sick & vacation time was tacked on - so I had something like six paid weeks coming to me! Hope you get that lucky!
