Weird interior electrical issues

My husband replaced the cigarette lighter fuse (15v) with a 10v fuse. That night at a store I accidently left my lights on for a short while. When I saw this I immediately started the car to make sure the battery was not dead, and it did start. After letting it run a minute I turned the car off and when I tried to lock the doors with the driver's side button the electrical door locks did not work. Approx 5 minutes later I started the car to drive home, and the dash lights were dim, especially when coming to a stop, and the car would act like it wanted to stall. The radio will not power on, the dash clock has no power, and the climate control keeps resetting itself when I start the car. The electrical door locks only work on the driver's side if the ignition is turned on (both inside lock button and outside manual lock), but the locks work from the passenger side regardless whether it is turned on or not!
When I had returned home, I removed the fuse we had replaced and left the fuse port open, the same way it had been initially before these problems started. We are unsure if the fuse replacement was a coincidence or an instigator of the problem.
The car previously had a vacuum leak, but the poor idle wasn't a problem before this event occurred.
My husband is a mechanic and he is somewhat stumped. The alternator is working properly and the battery tests good. We read on another board mention of a BEM, so our question is whether this could be the source of the electrical problems we're experiencing?

If it makes any difference, the car was manufactured in Australia.