Does a power supply draw only as much power as it needs?

When you buy a 500W power supply that means this PSU can deliver a maximum of 500W ! So if yours motherboard + HDDs consume 100W then your power supply will get 100W (+ a negligible cost of transformation ~10%) from the power plug !

It varies according to the power efficiency rating of the PSU, in short - yes, it only draws the current its asked for by the computer, but the efficiency of converting the power from the wall socket to something the computer can use is roughly 80% (ie your PC uses 80W, it'll draw 100W from the socket)

Look for APF (active power factor) for more details. This efficiency rating varies also according to how much power is drawn and the 'size' of the PSU, eg a 1000W PSU will not be very efficient when supplying 50W.

Yes, a power supply draws power relative to how much is being used. So if your PC hardware is only using 200W, your 500W power supply won't draw 500W. How much it draws will vary from power supply to power supply.