When I turn my BB off and I receive a text during that time, when I turn it back on it shows me that I received the text at the time that I turned it back on, not the original time. How can I change this? Also, what is the Blackberry Messenger and how does it work? thanks

You cannot change this. the time you see is the time that you received it.
its always been this way.

BB messenger is like any other IM client, except you use the PIN of your friends BB's and you can chat to the,

If the correct time you received the message is that important to you then don't turn the device off. If you don't want to be disturbed at night, then use a different profile like "Off" or "Phone Only". I use phone only when I travel so emails won't wake me while I'm sleeping but I will still get phone calls.

BBM only works between you and other BB users. The difference is that it uses data, not text messages. You must have a Data Plan in order to use BBM.

Bill J