All of those things are no longer true, based on my casual reading of the New York Times.
(Note - I was also told to use "He" as the generic case for singular person. Outside of english 11/12, I've never used anything other than "they" - and have never had anyone comment on it. "They" as the singular person form is fine, and avoids the gender confusion.)
If you know someone rather well, you say
"Wie geht es dir" - "How are you?"
but if you don't know him, you say
"Wie geht es ihnen?", which literally means "How are they?"
Also, back in the old days, you would talk to the nobility in plural.
"Wie geht es euch?", there is no equivalent in English I guess, since you is plural and singular, "How are you?"
But it's perfectly correct: English writers have been using both the singular 'they' continuously for hundreds of years (14th century?). It also has equivalents in other west European languages (e.g. the German neuter gender and the French ils for a group of people of indeterminate gender), so it's not an English invention either.
And it's totally fine "They are" has been used in the way for hundreds of years.
"Though semantically singular or ambiguous, singular they remains morphologically and syntactically plural (e.g. it still takes plural forms of verbs)."
Thanks.