I was wondering if a "mermaid city" (where people lived in the ocean and somehow breathed underwater) could have any means to create or use electricity. Thanks!
It is feasible - but would be a lot harder than it was for us.
Conductors - It wouldn't be an easy task for mer-people to smelt copper or other suitable conductors underwater. High temperatures under water are difficult to achieve. A possible solution would be to use metals that can be found in the environment - so maybe gold wiring?
Insulation - A major issue is that the oceans conduct electricity pretty effectively. So all circuit elements would need to be well insulated. Bare wires; open sockets; a 'bread-board' of components sitting on a table; a battery stored on an underwater bench - none of the above would be practical. Possible solutions might be insulating everything, or working in 'vacuum vessels'. In principle it might be possible to replace the sea water in a room with pure distilled water (which has much lower conductivity).
Generation - Something like a lead-acid battery would be feasible (assuming the mer-people can also solve the problems with doing wet chemistry underwater). Hydro-power is obviously impractical, as would be generators powered by fuel-burning motors. Geothermal generation from deep undersea vents might be practical; similarly nuclear power. But any generator would be complicated by the much higher frictional losses when operated in water - so generators and other rotating machinery would be best operated under vacuum.
Reticulation - Probably no specific issue here so long as the insulation problem had been solved. But plug/socket arrangements would need to be clever in order to allow connection/disconnection without producing short circuits in the surrounding water.
Safety - Hideously unsafe unless limited to low voltages.