2. How can I check AC balance? Is it noticable in Hlog, QLN, SNR margin graph?
No, the graphs will not provide any information. Hand-held testers, such as a
JDSU HST-3000c or an
Exfo AXS-200/635, will have the means to qualify a circuit. They have an option to perform a Pair Quality Test (PQT).
1. Why would you expect to 50 Hz common-mode "hum" affect the ADSL service? What way, if it would be not noticable in QLN?
An induced longitudinal signal (common mode signal) could bias the differential input circuit and distort its operation, to the detriment of the wanted differential signal, for example. A well designed and optimality constructed differential circuit should be capable of rejecting a longitudinal (common mode) signal. But no circuit will ever be perfect. So it would be sensible to ensure that any influence of an unwanted signal is minimised.
Why does switching off can be heared in the AM radio on the significantly higher frequiences if mains frequency is 50 Hz.
It is due to the spark that is generated when the current being drawn by the load is interrupted by the act of switching off. The original radio transmitters were spark devices -- they radiated significant energy across the entire radio spectrum. There were true broadband signal generators, without any means of real tuning the signal to a specific frequency. (Perhaps you will find it interesting to read about
Marconi's original radio experiments and his very high voltage spark transmitters.)