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No damage will occur. However the Motorola's tend to be picky. They may reject any USB charger which is not the original - and not charge. The Blackberry could care less it will take any USB charger. Notice when you go to a Radio Shack Store they have different model chargers but they are all USB.
Turn off the bluetooth if not in use. Turn down the display brightness. And if not using GPS, turn off the locator. Those three things will Greatly help your battery from dieing so quickly. If none of these seem to work, you may have a bad battery or charger.
While placing your SIM Card into the BB should allow you to send and recieve calls and send/recieve email/messages, you will not be able to utilize GPS-centric programs and features on your blackberry device because the network will not understand the software and the BB will not be able to download certain information streams because they will not be available from the network. I strongly suggest getting a plan with the company the BlackBerry is designed for. You can tell by the model number. For example the 7510T is for t-mobile, the 7510C would be cingular. If the model is the 7510A (which stands for all networks) it's the model thats most functional with Boost. Still I suggest signing up with T-mobile or Cingular.