My new apartment has no 3 prong plugs with ground

You have an advantage over the rest of us. The screw in fuses are better quality than the cheap metal they use in the circuit breakers and by floating the ground on your equipment you will most likely get better sound. The real challenge will be the room itself.

..just replace the wall outlests (easy to do). The 3rd (ground) might or might not be grounded...usually the box itself is grounded and therefore the plug will be grounded even if the 3rd wire isn't connected. Cheaters are no good..they ruin the sound.

The house is a duplex, our floor has 100 amps: 2 X 30 and 2 X 20, people below us have 140 for some reason. Maybe its their new kitchen. Looks like the dryer is on its own 30amp wring which is good.

I screwed the cheater into the center screw of the faceplate. Not going to mess with anything for now, the wiring is a nightmare in the basement.