Hi Audiendus. I study coordination (with 'and', not so much with 'but'), so I'll be happy to discuss this with you.
Regarding your sentences:
(1) Yes, I agree, 'normal' contrastive use of 'but'.
(2) That's probably an example of a correlative conjunction, with two parts, like "either... or" or "both... and", rather than just 'but' on its own. So aside from there necessarily being some historical explanation for how that usage developed, it is a distinct construction with different properties. (Within it, 'but' does seem to have essentially the same meaning, though, right?)
(3) This one is fascinating to me. I'm not familiar with that expression. Do you know which dialect it comes from? Is it possible it's from Irish English?
It seems parallel to a Celtic construction, with an 'absolutive' clause with a subject in accusative case plus description with no finite verb ('be' is omitted, while a lexical verb is in a non-finite form). This construction has been borrowed from Irish and Scottish Gaelic into Irish and Scottish English (and it has found its way elsewhere, such as I think some usage in Shakespeare's works). An example would be:
Tháinig Seán
agus é ólta.
'John came
and him drunk.' [='while drunk']
This has been discussed a lot as "subordinating-and" in the literature on Celtic languages and Celtic Englishes, and it has survived as an expression also in the broader Celtic-English diaspora (e.g., several American dialects). I have a number of references if you want some reading suggestions. (That's from a paper by Martina Häcker. One of her papers is uploaded here:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.524.7790&rep=rep1&type=pdf)
My research focuses on pseudocoordination, usually of the verb-and-verb type, such as "go and get" or "try and do" where 'and' is being used in some sort of subordinate (or just non-coordinate) way. This Celtic 'subordinating-and' is obviously similar (but with some different properties). However, at least within Celtic, it seems that
agus (plus cognates) originally functioned as a preposition that only later took on the coordinating function. So it was always subordinating, and this is a subordinating relic, rather than an innovation of the coordinator as subordinator (therefore arguably not 'pseudocoordination' per se). Of course in English this is due to contact, so you could say it's a coordinator being used differently, but only due to literal translation / calquing. (English 'and' also etymologically comes from a preposition meaning roughly 'after', but that's unrelated in this case.)
So by analogy I imagine that with 'and' used subordinatively like that, some speakers might also use 'but' in that way. (At the moment I can't remember seeing examples of that in Celtic languages, and it's certainly not a frequent point of discussion in the literature, but it may be used similarly.)
On the other hand, although that construction is exceptional and maybe related to the Celtic subordinating-and, there is another possible explanation. Sometimes 'but' means 'except', as in "I don't have any fruit but apples." (='I have no fruit but I do have apples.'). That usage does not typically allow for a finite verb ('but' is a sort of 'preposition' there I guess?), but it seems like a hybrid construction of that type. A related form that is grammatical but doesn't have quite the right meaning to my ears would be something like "It never rains but pouring". (Note the non-finite form as would typically be found in Celtic also. The finite form is anomalous for the potential Celtic explanation as well.)
I'd be very interested in more data like (3) if you have it.
