Restore iPhone backup to unlocked iPhone?

I have been using an old locked Verizion iPhone 4s as iPod. Recently got an unlocked tmoblie iPhone 4s, my question is: if I restore back up of old phone onto new one will the new one still be unlocked to use with a prepaid GSM SIM? (I.e. AT&T go phone or tmoblie prepaid)

You'll be fine. You're only transferring the data.

Yes. The locking procedure is independent of the content of the phone. It's in the baseband firmware, which is not change by a normal backup and restore.

Assuming it is a factory unlocked 4s then nothing would remove the unlock.