Web browser

Does att charge when you go on the bb web browser or opera mini

Not unless you have a data plan, but then again, there is a charge for that. So ultimately, the answer is yes.
If you don't have a data plan, you get charged per Kb.

BB web browser, if its HTML, only appears if you have a blackberry data plan. with no data plan it is either going to refuse the data connection, or charge per Kb