My new apartment has no 3 prong plugs with ground

Speak to landlord to go with the building CODE and to replace/rewire them ALL at once. Calling building inspector once in a while will stimulate the landlord's speed of action.

Ejs811, Look at your electrical panel. Sometimes it will state the capacity of your electrical service. Or, you can set up your gear and not worry about it. The only thing possibly drawing a lot of current is your amplifier and it depends on the load presented by your speakers and the volume you listen at. I would not count on your landlord rewiring any time soon.

There will be two mains fuses, at the top of your electrical panel. Read the sizes on those, to determine how much amperage is available, per phase. Outlet boxes in older homes ARE NOT USUALLY grounded. Especially if the wiring is knob and tube. Unless the wires were run through metal conduit(EMT), metallic liquid-tite, Bx cabling or have a third ground conductor to the box; it is NOT grounded. Grounding(running a pigtail) to the new outlet to an ungrounded box would be a waste of time/effort. Besides; the ground terminal on grounded outlets, is already grounded to the box through the mounting tabs/screws.