Since there was a Mirror Universe Vic Fontane (a live human rather than a hologram), I would expect there was a Daniels who was just a regular 22nd century enlisted man on the ISS Enterprise. I half suspect there was also still a human that looked like and had the same name as Jake Sisko in the MU, just Ben and Jennifer weren't his parents, and he was on Mars or someplace else.
The rules are subject to the whims of the writer. In 'Parallels' in one universe Troi has kids with Worf, two of them, in the Prime world she has none...yet unless you count the TNG relaunch novels when she and Riker breed.
My suspicion is that in the Mirror universe Mudd is a billionaire who rose to the position of Emperor by appealing to conspiracy theorists and xenophobes.
It could be that forcefields for inside of the ship was not know to Archer group at the time or the forcefields inside were off line due to systems being unhooked
The technobabble explanation is 'quantum resonance', so Sid Bloggs and co can only crossover to a mirror universe where an alternate Sid Bloggs exists; those where earlier divergences mean he was never born are inaccessible due to lack of any connection. Technobabble, but it sort of explains why there are only crossovers to alternates where the same people exist in different roles.
As to being able to conquer the Vulcans and others, it could well be that the MU Vulcan prisoners could have been "persuaded" to provide technical expertise and information. Earth already had warp drive, so this would enhance their own technology. It would definitely seem that the Terran Empire actually does little of its own scientific research, and seems to gain most of it's tech by theft or conquest. By the time of TOS, the Constitution Class still appears to be the top-of-the-line starship despite the Defiant being decades old, the only difference being that they probably have dozens of this class of ship rather than simply the thirteen. Another difference is that the Empire doesn't need to reverse-engineer the Defiant. Her databanks are filled with full blueprints and schematics for all Federation 23rd century starships, as confirmed by Khan in Space Seed and TWOK.
Maybe true but of this the mirror universe that Kirk ,Scotty ,Uhura and McCoy went into was one running without the Defiant being there. The one with Archer was another mirrored unverses an Empire that got the Defiant and there's one were no Defiant came to and it ran it's course in time and that's thexactly one Kirk came into.
They can be the same MU or two different Unverses or three or four or more if they are closely in experiences they are any number of possible unverses
The writers wish to lock down the number of possible unverses because they refusal to use the theory that said for each action there is oposet reaction and when you add each action a person make in a day were time and choices are add in to it you think it over
I am still of the opinion that Mirror "Vic" was actually Mirror FELIX (the programmer who, in the regular universe, created Vic). You'll notice that nobody ever calls MU "Vic" by his first name...
I don't even know what you're talking about anymore. Enterprise MU and TOS MU are the same universe, that is canon.