Eso is kind of lenient in its understanding of undeath, and to a much larger extent vampire blood lines. Different blood lines carry different powers, and in theory there could be a strain that does what his does.

That said, I think the reason the only ones that can control vamps are the higher ups is because controlling the undead is hard, very hard to do. Raising them is easy. Why would a necromancer spend years and years learning to subvert vampires and risk it failing, and their death, when they could go to a graveyard and get an army?

Best I can do without research, hope it helps!

a vampire, in TES, cannot be controlled by a necromancer, only if it was killed((again)) could a necromancer raise it, then control it
((even then thats sketchy, because i think vampires turn to ash upon re-kill, or at least a good portion of their insides do.))
but a priest can use 'turn undead' on the vampire and it will induce a supernatural fear in the vampire causing it to turn and flee, success of said spell determined by the tier of the spell used, and the strength of will of said vampire.

In relation to breathing, i think thats a BIG maybe, but even in past installments of the series, as a vampire, you still ran out of air when you were underwater, which seems to imply that vampires do indeed need to breath, and that the mere fact that they are a vampire does not gift them the ability of water breathing, or being breathless as the case may be.
Their bodies seem to function, mostly, as they did in life, as they gain benifits from normal food, rest, and potions. Though its obvious they cannot sate their 'thirst' with normal food, and must imbibe blood, preferably of creatures that hold 'black' souls, aka the races of tamriel. It should be noted however that a vampire does not need to Eat normal food, as the body, while gaining benifits, retains no sustenance from normal food. It could even be argued that a vampire does not truly need blood, as many cases exist in lore of vampires that had been without blood for centuries.

The lore behind Vampires in TES is confusing at the best of times however.

There are many holes in your friends 'breathless' theory regarding the lore of The Elder Scrolls series of games, It is ultimatly up to you whether you wish to allow it in your sessions.

Well, vampires do indeed have souls, they are in a state of unliving/undeath. Even undead, they still did not really die. There bodies where altered changing them. This makes it impossible for Vampires to rot, maybe shrivel up or look older or have veins showing or deformities. I think it depends on the amount of time ones been a vampire as well as the strain. As they grow older they get more benfits and become more undeathly. Not needing to breath, posion immunity more powerfull resistances but weaknesses.

Provided the vampire does not go feral. they could live for centuries. They are possibly more likly to be able to be controled by a command humioniod spell, but they would be restistant to this. I don't think they can be really controled by any necromancer spell, some strains can be feared by turn undead spells, or repel spells that repell undead. But some strains might be immune to it.

Vampirism is a mix between living and undead. They become undead but never died. So they are unliving. They might not have any pulse but they did not really die either because the soul never left the body. The condition changed the body into this state making it magical.

Oh here's a quote on vampires and breathing. To me it seems to suggest that the vampire in question did breathe while she was a vampire, but it didn't feel as refreshing as breathing as a mortal.

[After Serana is cured] All clean. I feel like I can breathe again for the first time since I was turned. The world is alive, and so am I, for once. - Serana