Don.
The anti corrosion oil was never used when I was on board,(almost 3 years) and I guess it was not used permanently, more like an "impregnation" of the steel/ castiron. We did not analyze the coolingwater but it it was no sign or smell of any contamination. In my part of the world direct seawatercooling was commonly used on diesels and semidiesels particularly in the fishingvessels without any anti corrosionprotection.
I guess the distilled water was primarily used for refill of the batteries, we never used same for drinkingwater.
During the WW2 real soap was rationed and hard to get and I remember the soap was not that great even in freshwater, so I guess the Germans used the shower just to have a rinse and cooling off, we did not used the shower, but during long missions we did most of the washing in seawater and you could have a special soap for that.
Although we had standard procedure to shut off as much as possible of the cooling watersystems going deep, I believe for the e-motors and thrustbearings the cooling circuit was open at depths down to 100 m.
We did not have any anticorrosion barrels on board.
We did not have any laundry facilities on board, however except for long missions, a submarinetender was usually in the neighbourhood which had the facilities, otherwise some of the worst clothings had to be dumped as you say.