To start, I am new to Pathfinder. My first character is the summoner that I am playing and trying to figure this out for - I'll recount what I've figured out so far in researching this;
From what I can gather, an Eidolon is a projection (an "aspect") of a stronger than normal outsider (read: not your average, mediocre animal summon) that the Summoner has bonded with. When an Eidolon is dismissed, it does not carry back any items or equipment in it's possession whatsoever.
My questions are as follows:
1) Just what in the seven hells is the Eidolon an aspect of, anyway? Any potential outsider on any potential plane?
2) Is consciousness shared between the Eidolon and the outsider it is projecting? If I find this outsider and wave at it, will it know who the hell I am?
3) Is anything I give the Eidolon (ability increases, skills) actually taken back to entity I am projecting? If I give it more intellect, does it keep it, or is that specific to the Eidolon itself? How the heck does that even work?
4) Does anything on the Eidolon get transferred back when it's dismissed? Injuries? Tattoos?
My end goal is to meet the outsider I am projecting as my Eidolon. To accomplish this easily, at 13th level I am taking Create Demiplane, and having both parties meet on that demiplane, which seems to be much easier and safer than plane shifting to the Eidolon's home plane and wandering around clueless in the 500 mile "close enough" radius that Plane Shift can land us in, provided my party can even learn where the Eidolon is centered in that plane in the first place.
My first idea was to scribe Plane Shift to my demiplane on the Eidolon's arms, and have it try to make a UMD check to cast after I dismiss it, but it seems the physical form it takes on the material plane is just an image, so the being would not receive the writing.
1. That is mostly fluff for you or the GM to decide.
2. see #1
3. It only affecta the eidolon. Basically the summoner is able to use more of the outsider's power to create more powerful eidolons as you level up
4. What happens to aspects does not hurt the original creature.
As for meeting the actual creature, that is up to the GM, much like who are what a witch's patron is, is up to the GM.
2. see #1
Are there no set rules on an "aspect" of an outsider? Is their memory/vision/entire conciousness not one and the same?
If I teach my Eidolon how to write a scroll, can it retain that information in it's true form after being dismissed?
There are no set rules on it. The games uses it as mostly fluff. You could just as easily say they came from some demon lord, or a deity sent the eidolon to help you, and so on.