As for the group in the bathroom -- I'm convinced that it is entirely by design that that group is not connected to the ground fault circuit breaker. You see, the voltage difference between the two phases is 230V -- but that does not mean that one phase is 0V and the other is 230V. It could just as easily be 50V and 280V!
That's not much of a problem, unless you also have a connection to the earth -- which is 0V.
Everything in the bathroom is connected to the earth by a separate wire. Which means that, even in the even of the ground fault circuit breaker being tripped, you could still have some residual current running from the lower phase to the ground -- through you.
A ground fault circuit breaker also trips if there is current fed into the home from outside, so the cause of the problems might lie outside our house. We'll see what happens with my computer off for the night.