can one of you please answer this "very important to me" question..and I really need these questions to be answered by someone really knowing the grammar of English, not by a student or "give a shot" teacher..the question is that:

what are the structural differences among rather, quite, pretty and fairly?

I want the responder to say like: pretty takes adj, not noun; quite can be used before nouns adverbs etc..

note: I've been scanning forums and books all night and got some answers but not satisfied..trying to make some generalizations for my job, I'm a teacher also, so I want a better teacher teach me..thanks in advance..
I assume that you mean the adverb definition of "pretty" (It rained pretty hard today.)
All of them - rather, quite, pretty, rather - are the same part of speech (adverbs).
Therefore structurally, as adverbs, they can modify adjectives, adverbs or verbs.
In fact, they can be used interchangeably in some cases:
I know him pretty well.
I know him quite well.
I know him rather well.
I know him fairly well.

Other examples of different usage and shades of meaning will be found in a good dictionary. There are differences in usage, but this is due to the dynamics of language, not so much to grammatical structure. Dictionary.com is a rather good source, a pretty good source, quite a good source, a fairly good source.

(Pretty can have an adjective meaning - e.g. She's a pretty girl. )
From the collection of words you've chosen, it seems to me that you have the "+ adjective/adverb" use in mind, meaning, roughly, "to some reasonable degree". For example:

"He looks rather/quite/pretty/fairly pale." (+ adjective)

"He tires rather/quite/pretty/fairly easily." (+ adverb)

The words can have other grammatical functions too. Definitions and example phrases are at: