/6 puking problem

That waterpump has some long bolts in it that go into water. One may go into an oil passage.

I replaced mine a while ago. $24.00 brand new at Autozone. Mine leaked from underneath too, and the replacement was just the quickest solution and it worked.

One thing I did was accidentally pierce the small hose going from the pump to the head - it's about 2" long, and it was a very small cut. It leaked out when stopped, but when it pumped it sprayed like steam. Also the hoses attached to the pump may leak and then cohere to the bottom of the pump and leak at the lowest point.

For the oil -
Touch the back of the head when the engine is cool enough to touch, just reach your hand back there and pat the head, then pull your hand out, if it is now covered in oil, the valve cover gasket is leaking down the back where the engine is the lowest. You may also notice a significant mess on the passenger side all over your oil pump, etc. Basically if your spark plugs are covered in oil, something above them is likely leaking. Your drool tubes may be another culprite if you have them.