water pump replacement Options

[jdmcivic00]

i have the upper and lower timing covers off and the upper mount off the reason i am attempting to replace it is because it was overheating then the powersteering pump belt tore itself apart so i assumed with the overheating and the belt locking up it was the water pump locked up but when i took the covers off it seems to be spinning freely it also broke the balance shaft belt. i decided to go ahead and replace the pump since i already bought it and it was overheating before. the timing belt has just been replaced and luckily it didnt get taken out but the question i have is wat might have caused the whole thing and do i have to take off the timing belt to get the pump out because i havent done a tbelt before and im a little afraid that i might mess somthing up.