Uso do "for" em perguntas

Not only with preposition FOR, but other questions that may end with prepositions.

First of all, such questions (ended with preposition) are usually used in informal/colloquial language, in academic writings the normal the rearranging of the sentence.

Which car do you want to go in? (informal/spoken)
In which car do you want to go? (redone to formal language)

The sentece you brought up "How long is your appointment for?" (sic) doesn't seem grammatical to me, I think the author meant "how long is your appointment going to take?"

Or in another context "What is the appointment for?"

But "how long" and "for" in the same question seems a bif "off" to me. Perhaps being "off" was what landed you here... Even if you had that "je ne sais quoi" (jenesequá) feeling!.

Ref. grammarly
Ref. myenglishteacher.co

Keep in mind that sometimes even speakers of a language may use it without heeding grammar or normal usage, it depends of circumstances, etc. So, after learning English, then we might want learn what can go wrong in communication to communicate properly!