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I am trying to get a better understanding of the interactions of these four effects, because it seems strange how it works. My character is a Divine Hunter Paladin. The enemies are under the effects of Mirror Image and Displacement. If I use Divine Bond to add the Seeking special property to my bow, I gain the following benefit:

A seeking weapon veers toward its target, negating any miss chances that would otherwise apply, such as from concealment. The wielder still has to aim the weapon at the right square. Arrows mistakenly shot into an empty space, for example, do not veer and hit invisible enemies, even if they are nearby.

This seems like it would ignore the miss chance from Displacement, but I would still need to contend with the Mirror Image.

On the other hand, the last two sentences of Mirror Image says:

An attacker must be able to see the figments to be fooled. If you are invisible or the attacker is blind, the spell has no effect (although the normal miss chances still apply).

So, if I see what square the enemy is in, then close my eyes before firing my bow, I wind up with no miss chance (the Seeking property takes care of that), and I don't have to worry about mirror images? I can shoot better by blinding myself than I can when I can see? Something seems off about that.

An alternate interpretation might be that the seeking property treats mirror images as a miss chance (example: 7 images means there is an 87.5% miss chance), and therefore ignores mirror images. But, the effects of displacement and invisibility are explicitly called "miss chances", making me think that is a game mechanic rather than any arbitrary random mechanic that might cause an attacker to miss some percent of the time. This seems more consistent with logic (blinding yourself doesn't make you better at shooting a bow), but less balanced overall.

I could not find these specific interactions discussed elsewhere.

There are other threads regarding sleight of hand in combat when invisible, so I apologize for adding to the mix, but this is a unique enough circumstance that I figured it bears mentioning.

Ranged Legerdemain is a supernatural ability that allows sleight of hand at a distance. If I am invisible (let's say it is greater invisibility to remove the discussion of whether invisibility breaks when using Sleight of Hand in combat), what happens to the item stolen?

1. Does it simply appear in my possession?
2. It was not invisible when the spell was cast. Does it require a separate action to conceal it within my clothing to make it invisible? Or is it automatically stuffed in a pocket when it is stolen?
3. Suppose the attempt fails (the item is not stolen) and the opponent's perception check notices the attempt. Is the opponent "aware of my presence"? I am 30 feet away using a supernatural ability (so no verbal or somatic components to give away my position). How can I determine if the opponent is "aware of my presence" to determine if I can try again?
4. What if someone randomly shouts out "Thief!" during combat when I have not attempted to steal anything. Does that preclude my using Sleight of Hand at all in combat? Does everyone become "aware" of my presence, even though the one who screamed out was just guessing? (Is this a good party tactic to prevent the DM from ever using invisible arcane tricksters against the party? We just scream that at the start of combat and then we are all aware of any thief that may be about, and sleight of hand is impossible in combat?)
5. Should Ranged Legerdemain only be used outside of combat? The last thing I want to do is slow down combat to try to adjudicate who is aware of my presence, but if I can steal the enemy wizard's headband of vast intellect right off his head in the middle of combat, that seems like it would be a lot of fun!

These are my main questions. I am obviously not playing an arcane trickster for phenomenal cosmic power. I am playing it for some fun, unique experiences that no other character would even contemplate performing.

Suppose you are under the effects of a transmutation effect that affects your physical form (Enlarge or Reduce Person, girallon's blessing, etc.) when you receive the benefits of a polymorph effect (such as Beast Shape). How does the latter spell interact with the former?

Some relevant rules are:

Combining Magic Effects

Spells or magical effects usually work as described, no matter how many other spells or magical effects happen to be operating in the same area or on the same recipient. Except in special cases, a spell does not affect the way another spell operates. Whenever a spell has a specific effect on other spells, the spell description explains that effect.

and

Same Effect with Differing Results

The same spell can sometimes produce varying effects if applied to the same recipient more than once. Usually the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.

One Effect Makes Another Irrelevant

Sometimes, one spell can render a later spell irrelevant. Both spells are still active, but one has rendered the other useless in some fashion.

Now, if the spells were cast in reverse order, I would not have any confusion. The first quoted text would apply. A standard transmutation effect can augment your physical form, or whatever form you turn into, but a polymorph effect replaces it rather than augments it, and this is where I am confused. Does it replace even your transmuted augmentations with the spell text? Or does it only replace your base form, and any spell-related augmentations occur on top of that?

Example: You cast Enlarge Person on yourself. Then you cast Beast Shape I on yourself to become a Medium-sized animal. Are you size category Medium or Large?

It is not clear from the text of the Polymorph subschool nor from the text of specific spells in the Polymorph subschool whether or not type changes.

For example, if I cast Monstrous Physique, does my type change to Monstrous Humanoid? Am I immune to Hold Person? The spell specifies that you can gain subtypes (such as aquatic and amphibious), but those are very specific. Beyond that, it only says you "assume the form" of the creature of a particular type, but it is very unclear whether or not you gain that type.

Benefit of not gaining the type means spells such as Enlarge Person still work. Drawback is that spells such as Hold Person still work. But, it is not clear which way the rules intended.