Grammar question, please help?

"which" actually refers to the last independent noun in a sentence. In this case, it refers to the "letter." (English is in a prepositional phrase dependent on "letter").

The sentence is not grammatical unless you're saying the letter is exciting. If you are trying to say that "time" is exciting, then you must say "This is the first time I'm writing a letter in English and it's exciting!" or a variant thereof.

Well you could look at it like this. You could say it and then ask yourself the question. "This is the first time for me to write a letter in English, which is exciting." Then someone could ask, "what's (which's) exciting?" Then you answer, "oh, writing a letter in English for the first time." Yeaah? Do you understand what I mean?

So, there you go, it pretty much refers to the sentence, or is it a clause?

In that context, it would refer to "write a letter in English." Sometimes it could refer to a noun.