While the relationship between Kaku and Jabra wasn't that obvious (as Jabra was in bad terms with Lucci too), it is clear they were depicted in a way that mirrored the Zoro and Sanji dynamics, starting with the Doriki ranking and following by their clashes with the whole giraffe thing. About Mr.1 and Mr. 2, their animosity was well established in the bar and I recall the latter treating the former in bad terms in Impel Down (there may be more moments showing this but I don't remember them). I think it is safe for us to assume the pattern of relationships Oda has built with this kind of enemies with regards to Zoro and Sanji.
How you assume Zoro won't fight the Beast Pirates is unfounded and therefore irrelevant.
King and Queen aren't just arguing, they're showing a deep animosity that goes back a long way as they directly assume their respective idiocy and incompetence. They literally had no reason to be mutually mad to begin with. They weren't even arguing at first, they were scolding Jack and, out of nowhere, they both took the chance to talk shit to each other. That's hate, not some temporary bad mood, whether you like it or not. Queen was also hostile towards King's failure at sinking the Big Mom Pirates, by the way, so the only other moment we get to see them together they seem in bad terms too.
And guess who isn't a Sanji fan.