Teacher-chan

"Sakura-chan... ur late.."

-Teacher-chan, episode 3

Teacher-chan is a teacher at school-chan and Doctor-chan's cousin. He makes his first appearance in episode four when Sakura Katana-chan interrupts his class. He most likely teaches math.

Personality
He's not shown much personality besides the fact that he is empathetic when he explains what happened to Terezi-chan. He's similar to Doctor-chan, probably because they're related.

Appearance
He is a middle-aged human man represented by a stock photo. He has greying brown hair, light skin, and blue eyes with an average build. Teacher-chan also wears a suit and square rounded eyeglasses.

Doctor-chan
Not much is known about their relationship except that they're cousins. It was probably positive though.

Sakura Katana-chan
He tells her that she's late, which is probably a common occurrence. He also informs her of Terezi-chan's death and gets emotional, probably knowing how much Terezi meant to her. She also takes his class alongside Terezi-chan, Alloin-kun, and Skutch.

Karkat-kun
Karkat-kun is his cousin Doctor-chan's son, making him Karkat's second cousin. They both have most likely met but their relationship itself is a mystery.