People who identify with "they" might be uncomfortable with the idea of being associated with any gender within the binary. It can be hard to understand if you don't use they/them.
About the grammar piece: "they" can be used as a singular pronoun, and has been for a while! When talking about someone you don't know, for example, you refer to them as "they" but still use "are". I'm not fluent on how exactly it can refer to a singular object but still use "are", but someone can probably explain it. ^^
About xe/xer: It's pronounced "zee/zer", and it's another non-gendered pronoun, like "they/them"! I think the difference between them is simply that they're spelled and said differently, and xe/xer uses "is" instead of "are".
Sorry if I didn't answer everything!