Is there a time limit in this game?
If yes - how much time?
If no - is it possible to have everyone or at some point you will get "cut"?
Never encountered a hard time limit. Usually it won't take you longer than 3 years to do everything.
Some things and girls do have a time limit, some of them intentionally, some are bugs (don't ask me which is which). For example: After marriage, Samantha might get pregnant even before starting anything with you.
Even without any time limit, it's not possible to have every girl in a single run. Some girls get introduced or are date-able in specific paths or after certain points of other girl's stories.
Dream girl gets introduced differently depending how friendly or "friendly" you are with Sam, which could complicate things.
Kat is only there if you encouraged Bree to be a gamer.
You'll only encounter Camilla if your ex's sister goes to jail.
Also, each girl has 2 or more paths to follow. Getting to one precludes the other. My suggestion is to play the game once, without cheating, and after finishing, play it again in NG+, to see the different outcomes, possibilities, routes. (NG+ also keeps your money, stats and traits, so it's not as grindy as completely new game)