Car broke down, belt had broken...replaced tensioner and water pump (figured out water pump was shot and leaking, getting onto the belt and pulleys and caused the belt to snap)...after installing brand new water pump, i put coolant into radiator and water pump immediately started leaking coolant from the bottom. Any thoughts on what the issue might be?

 

Is it coming out the weep hole?

 

no, out of the bottom of the water pump itself....maybe i need to use gasket adhesive, or a different torque wrench to tighten the bolts more?

 

It couldn't hurt. Lots of parts these days use cheap gaskets. Could be you had one of them.