I have come across at least 2 words: pila and fregadero. Do they really mean exactly the same thing or are there any subtle differences? Can they also be used for the washbowl that is not in the kitchen? Are there any other words in Spanish for the sink or washbowl or wash-basin?
Both are ok, it depends on where are located at your house.
Pila is according to RAE:
And fregadero is a pila where to wash/clean. According to RAE:
In Spain fregadero can be outdoors at a terrace for example when you are speaking about the one you use to clean your clothers so you will hang the clothes out to dry, or the fregadero inside the kitchen used to wash/clean your plates.
Pila is in the bathroom.
About washbowl is palangana
I guess this is very region dependent. I understand "fregadero" because of dubbings, but in my neck of the woods (Argentina) nobody ever says "fregadero"; here it's "pileta de lavar" (or just "pileta"); "bacha" is also used.