It's not a pun. According to sources, it's abbreviated 鬼のごとく正しい ("correct like an oni", "demonically correct"). It's not a set phrase ordinary people recognize. The heroine somehow liked this funny phrase after seeing it somewhere, and started using it as a pet phrase.
I have no idea where that HEX in the English translation came from.
大した is used to express admiration for something one finds remarkable or extraordinary. 大したもんだ or 大したものだ is kind of like saying “You are something” but it sounds condescending. It may also be used sarcastically.
なんか is a word used to make light of the word before it. It's interchangeable with なんて here. なんな right after it is a contraction of なるな. See this answer for the rule.
So the sentence is basically 冷静になるな ("Don't be cool/calm") but with the implication that 冷静 is an undesirable thing to him for now. He noticed that the dispassionate and realistic ...
なんでい is the masculine form of なんだい,なんなの,なにさ, etc as explained in the comment. It seems to be a variant of the Edo dialect べらんめえ口調.
Without the context, the meaning is hard to figure out. Probably the phrase is used in a condescending manner.
The speaker probably does not like the basketball club, so they uttered the ...
This is a set phrase that literally means "That(it) is a big deal." But the connotations and actual meanings depend on the context.
A breakdown of the phrase goes:
considerable; great; important; significant; a big deal
You can use this expression to praise the someone else by marveling at their achievement.