Once the endgame starts, you're no longer in a sandbox. There's no exploring or trying out different things. Once the endgame concludes, the game's finished, there's an epilogue, you're given the chance to unlock new game plus (NG+), and then it's back to the main menu, no additional playing possible.
If you want to enjoy the game just one time and see/do everything possible in that playthrough, choose "no time limit."
If you want to play it as a game, and enjoy the challenge of trying to complete everything before time runs out, choose "with time limit."
New game plus has one additional LI character (no other changes to the story). With NG+, you also start out with the stats you had at the end of the normal game, and start out already knowing several spells that you have to discover and learn in a normal game. Not having to level up as much frees up a lot of time, so NG+ is more conducive to exploring everything, unlocking all the sex scenes, etc.