No, mirror images aren't enemy creatures

Sneak attack requires "another enemy". Mirror images aren't enemies different from you; they're in your space, and they "move with you", so they don't present additional threats.

In general, there's no strict definition of "enemy" provided in the PHB, but it's often used interchangeably with "hostile creature". So, as you continue to find ways to enable Sneak Attack for your Arcane Trickster, consider the Sneak Attack rule to be:

You don’t need advantage on the attack roll if another creature hostile to the target is within 5 feet of it, that creature isn’t incapacitated, and you don’t have disadvantage on the attack roll.

Mirror images aren't hostile creatures, so this won't work. RAI for allowing sneak attacks without advantage when an enemy is adjacent to the target is clearly that sneak attacks are facilitated by the rogue supplementing other party members in combat, so low-level illusions don't cut it. Note that you don't have to be in melee; you can stand back and snipe with missile weapons while your ally gets in close.

(As a general suggestion, I would work on using your Arcane Trickster's spells to buff yourself/teammates and make ranged sneak attacks rather than trying to make melee sneak attacks work without teammates to help you).

The assumption from RAW would be that both the "real" caster and the duplicates appear to shift about. Being confusing to the viewer is part of the magic. To answer your points one by one:

1. Since images overlapping themselves exactly would look like a single image, we must assume that "the same space" refers to the space controlled by the caster (a 5' x 5' square if using a grid, or the narrative equivalent if using Theater of the Mind.

2. If the targets are constantly and randomly shifting, then logically, the attacks must be distributed randomly to model this. Assume that it is happening at a rapid and confusing speed, so that someone with two melee weapon attacks for instance cannot be sure that the person they hit last time was the one they are striking at next.

3. Many spells that require saving throws are area effect. For those that are not (example: Hold Person") it can be surmised that since no attack roll is required, the magic does not find a person through locating them as a target in a three-dimensional space, but as a metaphysical target, i.e "I want to affect that wizard. I know which one it is; so that's the one my spell will affect." If you need help visualizing this from another, non-D&D, point of view, consider the "Accio" spell from the Harry Potter books. Harry can summon his broom, his specific broom while fighting a dragon. He just tells the spell to bring "his broom" to him. It doesn't matter that he doesn't know where it is. Getting the subject is part of the magic.

4. It's a visual illusion, designed to confound sight. Other targeting senses are unaffected.

5. This is addressed in point #1.The illusion is deliberately designed to confound this sort of attempt, otherwise it would not work as described.