Yes. The faster the motor spins, the faster the alternator spins as well but since the car is using more power as well it is the same ratio of charging/using power as at idle.

RPMs is of little factor of performance. Its "demand" that determines the output: heater /defroster fan on high, stereo CD player, A/C, headlights, rear defrost, interior lights, dash lights, moving power seat, heated seats, heated steering wheel, etc, all put a demand on the ALT.

Yes, as it's dependant on engine revs, when you are driving at high revs it will charge faster than with the same load while idling!

An alternator will put out from 13.5 to 15.5 DC Volts at idle and at high RPMs. However it will put out more Amps at high RPMs than at idle.

alternator output increases with engine speed