There is a subtle, but crucial, distinction here that makes things clear: between letting rage expire and choosing to end your rage. The former is not an action, and happens automatically just before your turn starts unless you spend a round of rage to prevent it. The latter is a free action, which must be taken on your turn. So if you prevent rage from expiring, you have to spend a round of rage. If you then end it as a free action, you have still spent the round of rage.
If you end your rage early as a free action, you forfeit any remaining time in the rage—because that is what it means for rage to end. You aren’t suppressing it and resuming it, you’re ending it. So if you start the rage again, even if it’s in the same round, you have to spend another round of rage, because you forfeited the last one and it no longer matters that you already used a round of rage—that round is gone.
All of this is the technical details behind how the result everyone kind of expects is implemented: if you don’t use your rage for anything, then it shouldn’t consume a round of rage. That technically means you’re supposed to let it expire, rather than sustain it and then end it as a free action. But so long as the rage hasn’t seen any use—the free action is the first thing you do in the turn—that’s a semantic difference that can, should, and usually is ignored.
The reason I want to highlight this subtle distinction is because it provides a clear answer to your other scenario: wherein you have actually done stuff with your rage. Unlike ending the rage immediately at the start of your turn, which is effectively identical to letting it expire, doing stuff means you must have sustained your rage into this turn. Thus, you must have consumed a round of rage. If you want to forfeit the rest of the round to turn off rage, you can, and if you want to start a new rage, consuming a second round of rage for the same round, you can do that too (assuming some solution to the fatigue problem), but you have to pay for it.