I just browsed through a few specifications, and it says the heating power is designed according to DIN4701. Is that okay?
Sort of, DIN4701 was valid until 2003, afterwards it became invalid. Simplified methods are still based on it.
Since then, the heating load is correctly calculated according to DIN EN 12831.
You probably just found a few very old performance descriptions.
Is a hydraulic balancing of the underfloor heating always done or should that be stated?
Hydraulic balancing is not legally required. However, it is a prerequisite for funding.
Apart from that, a heating system without hydraulic balancing does not make sense. For safety, the hydraulic balancing should be explicitly stated – because, as always, you only get what has been agreed upon in writing.