There's no time limit to the game, though Corruption creeps up at a slow and steady pace so theoretically on a very drawn-out game you could run out of mental changes, Corruption would overflow and you'd get the Game Over ending. How long depends on your other Corruption sources like H-scenes, removing the collar and doing Vice actions.
Aside from some early-game Earth scenes, no events are tied to specific days either.
There are a few game mechanics that look at how many days have passed. Most importantly I suppose, demon generals become stronger after day 100. Which is irrelevant if you're willing to use Star Knightess on them. Overall, nothing to stress about. I recommend not following a step-by-step guide, especially since game mechanics are changing pretty frequently. Check out the
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if you need help with quests.