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.

Passive Checks (page 162, Player's Handbook) says

A passive check is a special kind of ability check that doesn’t involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster. Here’s how to determine a character’s total for a passive check: 10 + all modifiers that normally apply to the check

If the character has advantage on the check, add 5. For disadvantage, subtract 5. The game refers to a passive check total as a score. For example, if a 1st-level character has a Wisdom of 15 and proficiency in Perception, he or she has a passive Wisdom (Perception) score of 14. The rules on hiding in the “Dexterity” section below rely on passive checks, as do the exploration rules in chapter 8.

This rule is to allow the GM to be secretive. I would have no problem with a GM just rolling the perception check with advantage if he wants to, but by the rules the Owlbear in this example would have an 18 passive perception.