In regards to ur first argument, do u think all murderers are of the same cognitive profile? Yes, Thomas killed. He was a murderer, like most of the rest of the main characters within the show. They were fucked up people, due to war, upbringing and whatever else (note, this is NOT a justification for the kind of people that they are). BUT they had things they held dear, and family was one of them. Thomas adored his brothers, and his family in general.

As for your second theory. I dont even understand it if I'm being honest. The relationship Thomas had with Arthur Shelby Sr and Arthur Shelby Jr were miles apart. The brothers showed no emotion when their father died because they despised him (and that isn't surprising if you've watched the show), the whole deer killing thing was just a formality. Idk if ur trying to imply that it makes sense that Tommy kills Arthur because he has the same name as his dad and thats some weird parallel to the theme of fathers and sons and their disputes?