Can I buy a cell phone from a company other than who my service is with and be able to use it?

Answer 1

Depending on where you are - it always cheaper to buy the phone from your service provider. Where I am, sometimes you get the phone for peanuts - they just want your continuity with the subscription of line, that's where the money is.

Answer 2

Yes, as long as:
1. The phone has the same network specification as your network provider and
2. the phone is unlocked/open line

*This is for GSM Phones. I'm not familiar with CDMA.