Definitely invest in one of these. I always plug test receptacles as the electrician may have the breaker off or not connected yet within the panel (especially within new houses).

Sounds like a lot of the wiring is completed with old 2 wire without a ground. We run into this quite a bit around here with houses built within that time frame. The proper way to protect this (without running all new wire) is to add a GFCI receptacle. I don't know if that will solve the fault problem the UPS is showing (it should) but at least the receptacle is safe.

I would definitely be calling an electrician in to look into the wiring of the house. They should plug test everything and take apart any receptacle that doesn't properly to find out what is happening. There problem may be as simple as a broken ground within the panel or as advanced as the whole house used un-grounded wiring.

As for the receptacles being on with the dimmers, this was also done a lot around here back in that time frame with switched receptacles for lamps. Usually only 1/2 the receptacle was switched and the other half had constant power. Simple fix is to replace the receptacles and wire the switch wire together and leave it capped in the box.

The $hitty work we see from old houses and home owner electricians is astonishing and is surprising that the houses are still standing with the amount of fire hazards or almost fires (seen arcing in boxes with now covers sitting in insulation).