The standard word in the UK is "hall of residence". This refers to the whole building and houses a large number of students. Halls can be divided in different ways, typically into floors or groups of rooms that share the same common facilities, like bathrooms and the kitchen. In most halls, each student has their own room. I remember sharing my own room in my first year at university, but I would say that this is less common now.

Yes, a residence hall room would be a room where one or two students live in at the university. I have actually never heard this word, but I am American so that might be why. They are also called dormitories or dorms for short.

No, we wouldn't say that. 'Residence hall' is a term used in the US. The British term is 'hall (or halls) of residence'. If you wanted to make a compound noun to refer to one room, you'd say 'hall of residence room' If the context is clear, you could also shorten 'halls of residence' to simply 'halls'. For example, a student might say, "I was in halls for my first year, then moved out into a flat for my second and third". So you could refer to this room as, for example, 'my room in halls'. I googled lots of sites about student life in the UK and got plenty of examples of 'room in halls'. NB We don't use 'dorm' or 'dormitory' in this context in the way that AmE does. In a UK context, a dormitory is a large room with lines of beds in it - like in Hogwarts.