That ~9kW is probably split over 3 phases. Here you have 3x20A main breakers and then each circuit has a 10A or 16A breaker. So about 3.7kW limit for larger appliances (16A * 230V) on a single circuit, but should not exceed 20A on one phase. Stoves can be connected to 2 phases, 400V and get 7.2kW.
In the Soviet system, usually not. There are often several downstream circuits with their own 20A or so breakers and wiring (e.g.: kitchen stove, normal kitchen sockets, bathroom sockets and lighting, other rooms’ sockets, everything non-wet lighting), but each apartment is normally supplied from a single phase. On the other hand, different apartments on the same floor (or different single-family homes on the same street, etc.) might indeed be supplied from different phases. Normal (Schuko) wall sockets are most frequently 16A (so yes, 3kW kettles max), stove sockets (and circuits) might be up to 32A, still single-phase.
(That’s not to say the system is ideal, of course. E.g. GFCIs have become common only in the past fifteen years or so, and in a country-home setting I’ve actually encountered disposable screw-socket [IEC 60269] fuses.)
