If I want to make more than one private key with Bitaddress, do I need to reload the page each time and keep moving the mouse to generate the randomness or is doing it once enough for multiple private keys?
If I use one of these private keys, can some "hacker" generate any other of my private keys since he can reverse engineer the randomness?
You don't have to reload the page. No, a hacker cannot correlate the keys from one session as they are all random and not deterministic.