The water coming out the exhaust *could* be normal cold start condensation. Was it dead cold when you started it? If yes then it's probably just mixing with oil in the zorst.
That being the case, maybe one of your oil lines is leaking. The oil is misting and getting into everything under the bonnet, even the induction system. This would explain oil everywhere including exhaust. It's insidious stuff oil (that's it's job!). It gets everywhere and you don't need much of it to make a huge mess. The puddle may be from the source of the leak when sitting and draining from the line.