Try checking the drain holes on either side of the scuttle panel under the windscreen. They get clogged with leaves and stuff and the water builds up and finds a way in. Thanks to some channels in the floorpan, the water can also run in under the carpets and can gather in the rear of the car as well, leaving the front dry and the back carpets soaking.
There's been numerous posts on the forum about the strange places water gets in, and this seems to be the most common.
As for oil, I leave that to the experts. I know nothing about the options list of early Golfs but in the heady days of the early eighties I would imagine a lot of cars had a nice vinyl toupee slapped on them. My mum had a Mk1 Fiesta with one ffs!
