Regarding to drawing a syntax tree, "there" and "everything" in linguistics is a "pronoun" or "noun"?
For example, 1. There is an apple. 2. It is not everything.
There is an apple is ambiguous in writing, but not in speech.
(This is normal for English sentences)
If it's pronounced with stressed there, it refers to the location of an apple, presupposed to exist in context. If it's pronounced with stressed apple, however, it refers to the existence (in context) of an apple, with no information about its location.
Indeed, one can say
a sentence where there clearly does not indicate location (because here does).
Don't worry about what to call these words. There are names, but they're not important. Besides, I bet they didn't give you a complete list of terms or how to distinguish them; they never do. Grammar books and teachers who go on about "parts of speech" just waste your time; learn the constructions and you can call the chunks anything you want.
But if you think of English grammar as
word, you're sunk; grammar has little to do with words -- it's all constructions. That's one reason you can't learn grammar from a dictionary, which deals with words one at a time.
'There' is a spatial deictic as that, this. Traditional grammar considers them adverbs. As for 'everything', it is an indefinite pronoun. It is different from other pronouns (object, indirect object, ...), because it does not share with them any kind of person deixis.