Is it true that there is an in-game time limit? I mean, like time will run out of the player is idle with the game running? For some reason, I seem to remember hearing something like that. Is this true?

When idle - no. This game is "turn based" - every action you take (moving through locations, taking items, using items etc.) counts as turn and certain things have turn limit. To be specific, three, I believe:

1. finishing the game
2. healing the curse
3. torches longevity (there is finite number of torches in game so you need finish before using them all)

The higher the difficulty the shorter limits are. Except the "normal mode" which has no limits I think (at least no for torches).