Jailbreaking may or may not be an option based on what version of iOS is installed. It seems that 7.0.x can be jailbroken with
evasi0n. If it has 7.1 I think you're screwed. Not sure about iOS 6. There's a bunch of different tools for jailbreaking iOS 6 but I suspect there are subtle differences based on what specific version of the OS is on the phone.
The iPhone 4 came in both CDMA and GSM models. They look almost identical but have different model numbers printed on the back: A1332 (GSM) or A1349 (CDMA). You can go
here for details on the two models.
Unlocking is a whole different matter. I gave up on the jailbreak/unlock game because it became way too tedious worrying about each subsequent update to the OS. My solution was to just get a permanent unlock. If it's a US phone, you should be able to get it unlocked since it's more than likely past the initial contract period. There are also permanent unlock solutions on the net. I've used this site:
My IMEI Unlock. It's a true permanent unlock. Can't be undone by Apple.