When I quick save a game, and then start another game but don't end up quick saving that one, will my quick save of the previous game be deleted?
If its in the same mode, yes. If you quick save a game in standard, then go to play an easy it wont be deleted. If you quick save in standard and wanna play a different game in standard, it will say you have to delete the quick save in order to start a new one.
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I figured out that much, but I started a new game even with a quick save existing, but the power in my house went out. When I managed to get back on, I saw my quick save still existed...
Your quick save isn't overwritten unless you finish any game in the same rule set tour OR if you quicksave in again in the same rule set tour.
You could probably quicksave scum the game if you really wanted to.