You invite Emma to the west wing of the manor when you're done with her story.
Side girls you can invite if you fix the east wing.
You get two from the main story fey lead, if you choose to save them.
You also can get one from Roxy's story, if you make the right choice.
There's also Jessica's friends, you have to do their second events and then ask Jessica in the kitchen to invite them.
As for the events...
One appears later in Jessica's story.
Another will leave a message for you in Jessica's office.
The last one goes shopping at night.