Could my problem be greater than a water pump or thermostat?
I would suggest having the computer codes read. If it shows that the Temp sensor is reading too high, then yes, the cause could be from your water pump. Have the Codes read to be sure.
Yes, there could be a hole in radiator, or in hose/s to/from radiator. Have it repaired, ASAP. Experience over the years have taught that 'radiator repair' liquid does not work.
Well first of all thermostates don't make leaks, -- unless they don't open, in which case boiling makes water run out! And of course it could be waterpump, it could also be radiator hoses, and radiator itself, as well as heater hoses, and heater core! In extreme case it could even be head gasket going bad! (But defiantely it will be under the hood!) You just have to check things out an see where it is coming from! Waterpump has a weep hole underneath main housing, -- if it is dripping from there,- the seal in WP is bad. But rest of things should be easy to see if you look carefully! If you have very much water leaking get it fixed quickly, and keep it full, and watch temperature carefully, if it starts overheating shut down engine quickly! If you drive overheated you WILL blow head gasket, and if going even further- too hot, it will expire engine! This is very expensive!