Toko: The difficulty that many students of English encounter is the misconception that every word in English has an absolute and precise meaning which is distinct from all other words. That is an error in understanding. All the qualifiers you cite here, have similar meanings. They are not intended to be precise in their meaning, but to show emphasis which is itself, imprecise. We can say for example: "Your sentence is ...[quite, rather, fairly, very, somewhat]...interesting!" You might think of the words this way. They are show a general emphasis upon your subject. If I write about your question as quire, rather, fairly, very, or somewhat, it may be regarded as a form of "politeness" to you. It is a way of suggesting that your question is not superficial, petty, meaningless, or just plain stupid. So that if I employ these qualifiers, it is an encouragement for you to discuss your subject. Another way of expressing the same meaning would be a sentence like this in response to your question. "That is a most interesting question, Toko." So do not conceive of the meanings as different. They are similar. I could say; "Your question is brief Toko." That is a raw statement of blunt fact. That might understood as a kind of criticism of your question. However, I do not wish to be understood as being "critical". Therefore, I might use one of the qualifiers as a form of politeness, or in another context, rhetoric viewed as a "flowery" or pleasant speech.

Quite means very. Rather can also mean very. English is fairly difficult means English is most times difficult but not often. English is somewhat difficult means English not difficult but not easy. But is is more often difficult than easy.

I would rank them in the order you have them: quite = most difficult of these four choices rather fairly somwhat = least difficult of these four choices However, I do think that "rather" and "fairly" are very close in definition. Also, "rather" is sometimes used when you want a sarcastic tone.