Disclaimer 1: I do morphology, not syntax.
Disclaimer 2: The theoretical stuff is Chomskyan syntax, not proven fact.
In any case, the need for do in English is commonly known informally as "do-support". In Chomskyan syntax, the need for do arises from the fact that there is no movement from the head of the Verb Phrase (VP) to the Tense or Inflection Phrase (TP or IP) in English (in contrast to languages like French). (The only exception is the verb "to be" — this verb does raise from V to T.)
So, I guess any English sentences that show a lack of V-to-T movement would infer that do-support or something similar must be used.
One possibility to show this:
- English: I often eat apples.
- French: Je mange souvent les pommes. (Literal: I eat often the apples.)
In English, this adverb (often) appears before the main verb, while in French, it (souvent) appears after the main verb. The reason for the difference is that the adverb is located between T and V in French, and the verb raises from V up into T, above the adverb. In English, the verb remains in place below.
Note: the following diagram is overly simplified so that we ignore that the subject noun actually raised into its position also — this stuff is confusing enough already :)
The issues with negation and question formation both follow from the lack of V-to-T movement we see with the adverb ordering. For questions, T moves to C, and so a helper verb is needed since the main verb never made it to T. For negation, I think "not" blocks the passing of tense features from T down to V, so do is required in order to host the tense features (e.g. "do", "does", "did").
Also note that when modal or helper verbs are used (would, could, have, be, etc.), the helper verbs start out on T, so there is no need for do-support.
Never is a negative time adverb meaning 'not at any time', but no/not (variant combining forms) is a much more versatile and important chunk of English. Not is just one of the forms it uses when it's a separate word, instead of existing combined in a compound or contraction.
It's the basic Negation marker in English. So it can be adjective and adverb, but mostly it's fused into phrases and contractions, of which never is one. Never is a contraction of no/not + ever, just like other contractions of no/not:
- never = not ever
- none = not one
- neither = not either
- nor = not or
- no way
- nowhere
- nobody
- no one
- nothing
There are corresponding contractions with the Negative Polarity Item any, like:
- anyway
- anywhere
- anybody
- anyone
- anything
which are Negative Polarity Items, like ever.
Ever means what *anywhen would mean, if there were an English word *anywhen that was as commonly used as anywhere; in the same way, both of them means what *all two of them would mean, if that phrase weren't ungrammatical.
More important, as a Negative Polarity Item, ever can only occur within the scope of a Negative Trigger (or, as in never, bonded morphologically to its trigger).
Thus, ever is fine in these 3 sentences, with Negative Triggers (has)n't, few, and doubt,
- He hasn't ever seen it. ~ Few people have ever seen it. ~ I doubt he's ever seen it.
but it makes the corresponding affirmative sentences ungrammatical, though they're OK without ever:
- *He has ever seen it. ~ *A few people have ever seen it. ~ *I think he's ever seen it.
Best Answer
As ruakh and Barrie have pointed out, but is a coordinating conjunction. Logically, it means the same as and, unlike the other coordinating conjunction, or, which is quite different.
The difference between and and but is not logical or even semantic, but rather pragmatic.
If A is true and B is true, both conjoined constructions in the set {A and B, A but B} indicate this fact. However, A but B carries in addition a presumption to the effect that the speaker did not expect B given A, or believed that A's being true would normally contradict B, or was for some other reason surprised that B is true in this context.
There is no special technical term to denote this except, possibly, contrastive. It is not, however, negation, of any sort.