he was breathing just fine if i recall
Gotta think about their argument in real time, he was only in there for 30-45 seconds tops. If Kakashi can't hold his breath for 45 seconds something a lot of children can do and anyone who trains their body should be able to do. But if no one was there to release the jutsu then he'd have been in there until he drowned.
We know he was at least a jounin by these scans and we know Haku killed Anbu members from Kirigakure. It's been said he was an Anbu and killed Kumade Toriichi a Tokubetsu Jōnin of Konoha during his time as an Anbu before joining the seven swordsmen.
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I think he was a jounin when he abandoned Kirigakure and that's where his rank would stay like Sasuke, he's technically still a genin because he hasn't passed any nations exams despite clearly being at a higher level, same for Naruto. Zabuza likely continued to improve after leaving Kirigakure so I'm comfortable saying he's s-rank to some degree and better than most the Akatsuki(Hidan, Kakuzu, Konan, Zetsu, Sasori, Deidara, Kisame)
My biggest draw to Zabuza was the graduation exam story and his memory of it, if any character in Naruto deserved their nickname it's the demon Zabuza.