As far as I can tell, not in the US. Open Road Films is a joint venture of AMC and Regal, but Open Road only has about 1% of the film market. National Amusements has a controlling interest in Viacom, which owns Paramount Pictures, but National Amusements only has about 1% of North American movie theaters. None of the big US studios own any of the big 3 US theater chains.
But yes, the accounting in the entire movie industry needs to be taken with a pinch of salt, and perhaps some mind-altering chemicals.
No, at least not in the US. In one of the key anti-trust decisions, the Supreme Court declared in 1948 that it was prohibited monopolistic behavior for a major studio to own a theater chain.[0]
https://en.m.wikipedia.org/wiki/United_States_v._Paramount_P....
While yes, what you describe is true - part of this has to do with the film rights pricing which is mandated by the studios/distributors, so even if a theater wanted to structure things differently, they could not..
Of course many of the major theatre chains are also related to the studios, so it gets a bit hard to see which end is up..
but I digress