I thought it was LAQUELLE lettre? Does the meaning change if the "la" is dropped?
Laquelle/Lequel(/Lesquels) = which one(s). Quelle = which. Saying "Which one letter?" has a different meaning from "Which letter?". Laquelle is often used with an "est," if I remember correctly: "Laquelle est ma robe?"; "Laquelle est ta fille?". If it goes straight to the noun, use quelle: "Quelle animal?"; "Quelle livre?" :D
Is there a difference between the usage of "what letter" and "which letter"? Both could be translated as "quelle"?
Yes, in French "Quelle lettre?" means both "What letter?" and "Which letter?" Context would be needed to understand which the speaker means.
DuoLingo does accept "What letter?" as a translation, as it should.
As for context, these example dialogues in English should help:
A: Did you see the letter? B: (not seeing any letters anywhere nearby) What letter?
A: Did you see the letter? B: (seeing some letters) Which letter?
In English, they have different connotations. I'm not sure about the French translation, though Duo doesn't seem to accept it, which probably means they're also different in French.
In english you might say, for example
A. Did you see the letter? B. What letter? C. That one,
You couldn't really exchange what for which in that context, i am not sure it is the same in french.
Because it is. "Quel/quelle/quels/quelles" translates as both "which" and "what".
Why is 'French' a hint for 'lettre'? In which context would this be used?
In French which must match the subject in gender and number.
"Quel" -> goes with masculine subject.
"Quelle" -> goes with feminine subject.
"Quels" -> goes with masculine subjects.
"Quelles" -> goes with feminine subjects.
Lettre is a feminine subject, therefore we use "quelle" to ask about it.