What's up CivicGil,
It's hard to tell where the leak is coming from on those pictures, it almost seems like it's coming from where the pump meets the block (gasket). Usually, when the pump itself starts to go bad, they start to leak from the weep hole and sometimes make noise. If the car has high mileage and the pump has never been replaced, chances are it might be on it's way out.
Since you did mentioned that the pump "leaks like crazy" when the car is on, this leads me to believe that it is the pump itself and not the gasket. Obviously, when you replace the pump, you will replace the gasket too. Make sure you remove all gasket residue and ensure that the block is nice and clean. If you're doing the work yourself, get a Haynes manual and follow procedure. The work is not really all that difficult but it is somewhat time consuming as you have to remove other components to get to it.
Taking a second look at the first picture, it does appear to be leaking from higher up, confirming my suspicion.
Regarding additional replacements or maintenance, you should check all your belts for wear, tears and proper tension. Replace your thermostat if it has not been replaced and refill with 50/50, not just water.