[Occasionally6]

If you have to brake and dissipate the energy, the extra energy stored in heavier rotating parts matters. If you don't, it makes virtually no difference in terms of efficiency; it's still there just stored in a different form.

For a given power input and final stopping point you will accelerate more slowly and decelerate for a longer period of time. You will be slower.

If you want to quantify the rotational energy it depends on the polar moment of inertia of the rotating object. Mass concentrated towards the outside of the rotating object matters more than mass closer to the axis of rotation. Losing a pound of weight off the tire will have more effect than a pound of weight off the wheel.