Is there a way to sync my contacts and calendar with my Google? I know on the AT&T Tilt II you could, but not sure about on the LG Quantum.
Yes. It was actually really easy - Windows has everything ready to go (including the m.google.com server pre-saved in the account settings form). It took no time at all to set everything up.
No idea. Perhaps try taking the google account of your phone and then putting it back on again. I've never had a "duplicate event issue" before, so I'm not sure if that will work or not. Let us know if it does!