I have a question: how do I get Emily (I think that's Mario's daughter's name) to join the farm? And who else can I invite to the farm? As far as I know, only Anna, Amelia, Katerina, Emily, and Phoenix are allowed.

Emma Route info is in the Guide & FAQ on the main page

Solo Route

• The following week, go to the Sauna and have sex with her again.
• After taking down Mario, you can invite her to the farm by speaking with her either at the Terrace or Library.
• After milking her a couple of times, her cow outfit will be purchasable via Clay at the Farm’s House.
• You can have a 3some scene (have variations depending on dialog choice) with Katarina if both have been invited to the farm and you have their cow outfits.

All the characters you can milk at the farm 

• Kirby
• Anna
• Amelia
• Emma
• Katarina
• Phoenix