Firstly the belt has several names...most commonly serpentine belt, auxillary belt and it's sometimes called a fan belt.
You should be able to tell if the belt is gone as you will lose power steering because it also is powered by that belt along with air con (if you have it).
You need to find out exactly where the water is coming from, it sounds like you are saying it's coming from where the rad pipes meet the thermostat housing (which is a kind of a straight but almost L shape bolted onto the engine). Find out whether the water is coming from the pipes (which may not be connected properly or split) or whether its coming from the metal housing itself.
If water is coming from the pipes, you will need to replace whichever one is leaking and also replacing the hose clips would be a good idea.
If it is coming from the metal housing your fault is probably a jammed thermostat which may have blown the gasket from the water pressure causing it to leak. In this case you will need to replace the thermostat and gasket which is an easy task. I can help you more if you can identify where it's coming from.
You should be able to fix this yourself as long as you have some experience with a spanner
and obviously don't forget to get that new belt. (make sure its the right one as they are all different).
Hope that helps and good luck fixing your ultimate driving machine
P.S. One small tip...buy a service/repair manual, they are lifesavers and can save you a LOT of money.
If anyone has anything to add or if i have made a mistake, please correct me, I'm only going by previous experience plus it's late and I'm tired lol.