The usual name for a bathroom or restroom was toilet.
Private toilets, such as in our hotel rooms, were just like home. (Granted, we stayed in nice hotels.) The following comments apply to public toilets.
Men usually rinsed their hands but seldom used soap (often there was no soap). They almost never dried their hands. Usually there was no means of drying one's hands except sometimes a seldom used electric dryer.
Sometimes men and women shared the washup area.
Men tended to stand back from the urinal.
Every public toilet I saw had urinals. I never had to pee in a trough. However, on the road to Daqing it was common to see men urinating beside the road. The Buddhist temple in Daqing was for female monks (nuns) only, and so there were no facilities for men. Men peed outside in the bushes.
The most unusual stall facilities I encountered were in the rest area on the road to Daqing. Presumably someone came along and cleaned it out once in a while, like a barn gutter.
While walking around Shanghai I saw a pay toilet with an attendant:
You'll have to ask Margaret about the female facilities. It didn't sound like home.