Answers:
If the mirror your fixing has no bracket's on it or no drilled fixings.options are double sided mirror pads or high grab mirror adhesive
If the shower is plumbed in correctly.its more than likely the temperature setting on the mixer valve needs adjusting
The most common problem with motorized valves or actuators is the motor itself .this can be replaced as a separate part ,if the valve itself is not moving then the body will need replacing.
The flexible tap connecters on the feeds to tap usually contain restrictors and or check valves these can be prone to blocking up/sticking
i would check that first