A character with they/them pronouns is referred to as a "guy". They correct them and the other person apologizes. They are not referred to with wrong pronouns or gendered terms again.
nico di angelo does not eat, as he thinks he deserves to be hungry (and he spent a portion of his life starving so he's used to it). he is working this out with his therapist, and is said to eat at the end of the book
A character does not eat a lot because they are used to feeling hungry. It is not mentioned in great detail outside of this chapter...
[MINOR SPOILER]
... and the character does get better and eventually eats more.