If I buy a Verizon iPhone 4, can I jailbreak it and activate it with another carrier?

It's new and is without a contract.

Probably

Definitely yes!

Jailbreak is like using an openline phone any telecom carrier could be used.

Using jailbreak phone.

No, but you cann UNLOCK it using unlocking utilities. Jailbreaking just allows for software modifications.

You can't. The carrier would have to do that seeing that it is a CDMA model.