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Can't say much for speeding things up but I would advise focusing on Kali. There's a serious money boost to be had in her story which takes away that grind at least.

Simply try to keep going with their stories. Some scenes require you to visit their rooms during a specific time of day so keep that in mind as well.

A third guest will show up once Ashley's friendship level is at a certain point. After that, when you buy the second floor, another character will be introduced shortly. Then three more will be added eventually depending on how many days have passed.

Just take it day by day and see where you go. That's the fun of games like this after all, not knowing what will come.

How events appear is explained at the very beginning of the game. Just wait a few days, and click "* Talk *" on their door. Other times, it will happen randomly in your room or something. Stats are never required for the story, you don't have to grind anything for the story, you just wait a few days after the last one.