"Where is the big door?"

Translation: Càit a bheil an doras mòr?

[DrDuthie]

Is there a reason behind specific use of "càite" as opposed to "càit"?

[silmeth]

They are the exact same word, just different spelling. Càite a is an older more traditional spelling, càit a is a newer spelling that explicitly shows that the vowel e disappears before a. The course originally used càite and is now switching to càit. Both will be accepted in exercises.