Relationships... hmm... Well, since Fumiko works/-ed in the Agrarian Zone, she can be friends/acquiantance with Peizhi. Fumiko does visit the Bending Arenas to cheer on her twin cousins so that could be another interesting source of friendship. 

Since Mei works in a tea shop in the Lower Ring (if I read that right, anyways, kinda tired right now from all the socializing in my Uni's orientation), Fumiko can be a regular there when she's winding down or doing her schoolwork away from the rowdiness of her home. 

If Fumiko's cousins frequent the healing area, that could also be the reason why Fumiko and Nilak know / acquainted/ friends with each other.

The Earthbender guy would be the type of person that Fumiko avoids though.