"One must answer the court's questions with due respect if they are called upon"
tl;dr: You sentence is grammatically correct and completely fine.
Using "one" with "their" is fine in English, written or spoken. "Their" is simply used as a gender-neutral pronoun in this case and doesn't necessarily mean "multiple people" (plural). It's not really uncommon ...
I'd very strongly commend using the shorted form suggested by user98746.
I'm not sure what is intended by this long form:
One must answer the court's questions with due respect in their case"
Who are "they"? The person answering, in the context of a case in the court? The court itself, who are entitled to respect, in their case, because of their ...
I don't think it (the "of mine" form) is particularly more or less formal. It may be slightly old-fashioned -- I see it a lot in novels from the first half of the 20th century, many of them British, but I also see and hear it frequently enough today. I have heard it enough (in mostly US English) and read it enough (in both UK and US sources) that I am ...
There is no such rule, either in formal or informal English.
There is a tendency for "going to" to be used to describe plans, but in many situations, both ways of talking about the future are possible and correct. A study of when "going to" is used will find lots of examples of it being used (both formally and informally) in situations when no clear plan ...
You cannot have 'not' + verb in this sentence. It is better to write:
“In the period that we do not (don't) enter, Romanticism, the Account
became the preeminent formula for literary production.”
You can see more about this rule here: https://open.books4languages.com/english-a1-grammar/chapter/present-simple-negative/