I would say that the most important thing about this turn is that it is made on one foot, not both, and as the feet are closing. By the time the heels are actually together, we are almost done, and the main thing remaining to do is to transfer weight forward (and to the other foot), to rise, and step out of the turn.
I don't feel the turn as being on the 'heel', but with a backward, rather than forward, balance, and once the foot has lowered, the foot is flat on the floor. Things feel a little different for the ladies, because of their shoes having a smaller heel area. The turn is commenced on the ball of foot, anyway, because we cannot step back to a flat foot, so it is the continuation of turn that occurs on the heel, but with the foot flat (ie the toe is not lifted up). When the feet close, and the turn is almost complete, the foot without weight is being held to the side of the weight bearing foot. The turn appears to be on both feet, but can't be: it it were, the toes would splay horribly.
There's no real answer to your other questions, because all depends upon the chosen choreography. Foxtrot has heel turns for lady in both natural and reverse turns, but we should not overlook the telemark and impetus turn families, and of course, the 'heel pulls' that gentlemen dance in Quickstep, Waltz & preeminently, Foxtrot (the natural turn, again).
A heel pull is often danced very badly, and the fact that it is a heel turn (ie has the same mechanics and weight distribution) but with the feet finishing apart, is often missed, and the turn becomes a side step with a brush action. They are the hardest of all the 'standard' turns, in my view, and a measure of success is whether the man is able to lead an undivided turn for lady (not, of course, in a QS Natural Turn at a Corner - the exception).