No and Not
Not is an adverb that negates a verb or an adjective. No is an adjective and therefore modifies a noun.
She is not tired. (not negates the predicate adjective tired)
Juan does not want to go out with Carmen. (not negates the verb does want)
He has no money. (no modifies the noun money)
Too and Very
Too indicates excess. Very indicates degree and means extremely. When very is used as an adjective it means "the exact one."
Both can be used as adjectives or adverbs. When used as adverbs they intensify adjectives or adverbs. Very and too are not interchangeable.
There is too much snow on the car! (too as an adverb modifies the adjective much and means "an excess of snow")
He was too fat to sit in the airplane seat. (too is an adjective modifying fat)
She has the very book that I needed for my paper. (very as an adjective modifying book and means "this exact book")
The test was very difficult. (very as an adverb modifies the adjective difficult)
Few and A Few
Few connotes hardly any.
A few is the same as some.
Both are adjectives used with countable plural nouns or can be nouns themselves.
There are few movies that I want to see this year. (few is an adjective modifying movies meaning "not many")
There are a few movies that I want to see this year. (a few is an adjective modifying movies meaning "some")
Many are called but few are chosen. (few is a noun. In reality the sentence is saying "Few [people] are chosen" with people being unstated but understood)