iPhone 4 & Non-Active 3G syncing to same iTunes acct?

I got my iPhone 4 today and activated it and uploaded all the settings from my 3g. Works great. My questions are, I have my 3G that is not active and is now acting as basically an iPod Touch...

1. Can I still sync it to the same iTunes account without messing anything up?
2. Should I restore the 3G to original settings and rename it - since both devices now have the same name?
3. Can I have an app I paid for on both devices at the same time?


Thanks,
Todd