The belt tensioner maintains the belt's tension, everything else is stationary. The water pump just failed extremely prematurely. If you get the pump from
www.oembimmerparts.com they sell pumps with plastic and metal impellers. So you can choose which one you think is best. The pumps on average last about 80k miles or so. It's smart money to replace them at or before 100k if it hasn't failed.
Find an independent mechanic that has good prices and treat him like family. The dealer will always over-charge. Changing a water pump takes at worst two hours, hardest part is snatching the fan off. The part cost $117 + 2hrs labor = $317 before a little coolant, tax and shop fee. Anything over $350 is pushing it. (unless you are in a 3.0 and the pump costs $180)