I know only about your second part of the question, sorry about first part.

As long as you are in DC voltage domain, the simple Ohm's law applies. When you come to AC domain, things start getting complex. Since the AC is alternating (a sine wave), the current drawn by various kinds of load on AC is not in-phase with the voltage, causing a phase shift between Voltage and Current. This phase shift, in turn causes many problems. Power factor is basically COSINE value of this angle (phase shift)

Ideally the power factor should remain at 1.0 at which the voltage and current are in phase, this happens only in case of resistive loads like old incandescent lamps, heaters etc. If power factor is 1.0, the simple Ohm's Law still applies and W = V x I (watts = volts x amperes)

Now if power factor is lower than 1.0, for example a 23W energy saver lamp has a PF = 0.55 typically, the electricity company has to supply you 23W/0.55 = 41.8 VA. In commercial or industrial usage, this loss due to low power factor is a financial loss to electricity company and they charge the customers.

In old days, the energy meters were Watt-Hour meters and for commercial / industrial consumers, WAPDA used to install MDI meters to check how much low the power factor becomes and this is still in practice.

Now with digital energy meters, this MDI (Maximum Demand Indicator) thing is built into the meter and consumers are automatically billed according to their power factor.