"They" has always (in our lifetimes) been used to refer to a singular person of unknown gender. For example "someone left their coat here. They must be cold"
Indeed. What's new is not referring to someone of unknown gender as "they", but rather people identifying as non-gender-specific, and wanting to be referred to as "they". That's the part that feels so awkward, IMHO, not simply they as one person.
No that's incorrect. Use his/he or her/she if the coat appears to be one that would be worn by a male or female. If uncertain, use male pronouns, which are gender neutral in that scenario.
Incorrect according to who? You? Your Sainted Mother? Sounds innovative to me, and hardly traditional. Saying male is somehow gender neutral sounds even more bizarre.
No, usage makes correctness in language, not people trying to invent some weird conlang they wrongly insist is correct English.
I must have missed the brief somewhere, but there was/is a very clear trend to replace the default male pronoun for gender neutrality with the female pronoun she. Just recently I noticed this in Judea Pearl’s Book of Why. When and why did this start happening? It feels so forced and unnatural. You can sense he’s trying to kiss someone’s ass or appease an authority. At least mix it up a bit at best if you truly give a crap.