Was this phone on BES? If so, then there may be IT policies that have disabled some of these features. If so, you may need to remove them. Remove IT Policy - BlackBerryFAQ
(Other FAQs can be found by looking at the menu bar found at the top of each screen and going to Blackberry FAQ.)
The other thing, if you have started using this on a different account, is to ensure that you do have a blackberry (not generic) data plan to take full advantage of BB features.
Unlocking wouldn't have anything to do with this. It only allows you to use the phone on a different carrier than it was originally locked to.