How do pilots in the US identify the circuit (pattern) height?
The Airport/Facility Directory (AFD) has that info. It lists the Traffic Pattern Altitude (TPA) in both MSL and AGL, as well as circuit direction.

QFE is not used in the US. So yes, you have to make the correction for field elevation. For example, an airport at 1200 MSL would have a pattern altitude of 2200 ft. (1000 AGL for props. 1500 AGL for Jets) and would be flown using that altitude on the altimeter.