The "regular" use of have is the same as any other main verb - as a main verb it can't form contractions questions and negatives, be used in short form answers or carry contrastive emphasis. As such it is now different from any other verb - live for instance - and uses the "dummy" auxiliary do for all grammatical operations which require the auxiliary form :
I have a question
Do you have any questions? / Do you live in France?
I don't have any questions. / I don't live in France.
I do have a question! / I do live in France!
But it can also act like the verb BE -that is, it has the grammar of an auxiliary even when it's a main verb :
I've a question / I'm British
Have you any questions? / Are you British
I haven't any questions / I'm not British
I have a question! / I am British!
This form is used - especially by the older generation (see the novels of PD James for someone who uses it consistently), but can often sound a bit archaic and over-formal. Its most common occurrence is in negative expressions like "I've no idea". These are very common whereas the interrogative form, for instance is much rarer.
To answer your questions directly :
1-OK, 2-rare but possible, 3 - much more likely in the contracted form unless there was contrastive stress on not - but this would again be rare, 4. terribly dramatic! If used at all, it would be much more likely to be in the contracted form Haven't we a book on butterflies somewhere? - but again, fairly rare.
As far as the regular version is concerned, they would all be the normal version, except that again the contracted versions would normally be used : We don't have any books on butterflies / Don't we have a book on butterflies somewhere?
Personally I always teach have as a regular verb, and introduce expressions like I've no idea as idiomatic "fixed" phrases.
