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.

Yes.

The intention is more or less to mimic a limited version of True Seeing, which provides Truesight, and it is worded similarly:

Truesight: PHB, page 185.

A creature with truesight can, out to a specific range, see...

Witch Sight, as you indicated, PHB, page 111

You can see the true form of...

If the spell or ability indicated you could "only see the true form of," it would have been worded that way.

Again, Truesight, PHB, page 185:

Furthermore, the creature can see into the Ethereal Plane.

Clearly, this does not indicate the creature can only see into the Ethereal Plane, as he would be then blind on the material. This further affirms the previous usage of the word "can."