Electronic – What do all of these symbols mean on an old power factor meter

Apparently you have a inductive load to a AC power supply, and want to cancel the reactive part of the load by putting a capacitor accross it. You mention values Rs and Rl, but since you provided no definition for these, we can't tell how they are hooked up and therefore their relevance.

However, if I understand the problem correctly, this is mostly about finding the capacitance that cancels the inductance. From basic circuits you know that the impedance magnitude of a capacitance is 1/ωC, and for a inductance is ωL. Setting these two equal and solving for C yields C = 1/ω²L = 1/(2πf)²L = 880 µF.

Improving the power factor reduces the losses in the wires bringing power to your load. That in turn might increase the power delivered to your load -- so would changing the voltage supply.

If your load has an automatic adjustment, it will accommodate. If it is something like a water heater, it will also adjust -- the heating cycles will become shorter than before because they will operate at a higher power level. Ultimately, the wasted power (in the wires) will be the savings.

Note in most home and office installations, you don't pay for apparent power -- just real power. In industrial installations, you may pay for apparent power. Regulations in some countries require loads above a certain level (typ. 50 W) to have power factor correction. This would typically affect computer power supplies and televisions.