If a Magus binds a Faerie Familiar, does it become capable of learning Magic Theory (and other skills), and thus assisting in the Lab?
In Mythic Locations there's a Faerie creature (the Worker Elves) with Magic Theory as a Pretense, is that Pretense of any use in the Lab? (seeing as it has an actual further power that specifically allows it to team up with other Worker Elves and to assist in a Hermetic Lab, separate from even as it refers to the Pretense).
If the Faerie actually learns, does it take, or does it lose its new abilities in the long run (in a similar manner to the bond decay)?
No, as far as I can tell. The familiar bond (as per the errata) allows magic creatures to learn as humans, overcoming their static nature; not faerie creatures. However, nothing forbids a Faerie Familiar from learning Magic Theory or another Ability as a Pretense, or even as a "real" Ability provided it has the Faerie Trainer Virtue.
A faerie familiar can use its Pretenses just as normal Abilities (subject to the usual issues of being recognizable etc.). So, it should be able to use Magic Theory to help in the lab the magus who has bound it. Note that faeries not bound as familiars in general can't do this, just as magical animals not bound as familiars can't do this... unless they have an appropriate Power/Quality etc.
Given that the familiar bond does not give a faerie familiar any additional ability to learn Abilities or Pretenses, those that it does learn while a familiar should be unaffected by the decay of the bond.
I would say they can learn this, yes. Acquiring a Faerie Familiar requires a virtue, implying that such Familiars are at least as good as vanilla ones. They shouldn't be nerfed just for reasons of a foolish consistency with RoP:F Pretense guidelines.
While I don't have an answer, I think I have questions whose answers will lead to an answer:
Would you give a Faerie Familiar the Personality Trait Loyal to (partner) +3?
Would you give a Faerie Familiar with Cunning an Intelligence of -3?
Would you allow a Faerie Familiar to understand the languages of its master?
Would you allow a Faerie Familiar to assist in the lab?
If all of these answers are "yes," why keep the entire rest of the section while singling out "Familiars can learn Abilities in the same way as humans" as not applying? If all the answers are "no," why single out that one sentence as applying while not the rest of the paragraph. The sentence doesn't place any restriction on the type of Familiar to make it distinct in such a way. And, as has been noted, it is certainly possible for Faeries to possess Abilities even if most don't.
I think the bigger question is whether it can use both or if this generates two separate scores- in short does the faerie inherently gain "faerie trainer" when they become a familiar so they can learn magic theory (an possibly other skills) as a human, or can they develop pretenses which also gain from studying? Personally I favor the first- they can learn magic theory as a human but at the cost of not being able to develop it as a pretense (i.e. raising it simply because their magus does, or anyone else whose score is higher than theirs and develops their score that season)
Magic creatures can possess Abilities; it's just that it's hard for them to learn them. The text tells us that the familiar bond makes learning as easy as it is for humans.
Faerie creatures in general cannot possess Abilities, so it's moot to ask whether they can learn them. The single exception is the Faerie Trainer Virtue, but even there, it should be noted that the spirit of the Virtue is not "this faerie can have Abilities" but rather "this faerie can have some Abilities, so that it can teach those to humans fulfilling its role of Trainer". While there could certainly be faerie familiars with the Faerie Trainer ability covering Magic Theory (the wise old owl to whom the apprentice of the Incomprehensible magus always turns to), I don't think this should be the default for all faeries.
I would add that while the inability to learn Magic Theory would be a big issue for magic familiars, I fail to see why it would be for a faerie as long as that faerie could have Magic Theory as a Pretense: a faerie that roleplays being a familiar pretends to know Magic Theory! In fact, you can probably concoct a single Pretense that covers the uses of both Magic Theory and, say, Organization Lore: Order of Hermes restricted to those activities in which a familiar is likely to use either.
My point was that upon becoming a familiar the faerie would gain the faerie trainer virtue, especially for Magic theory, and possible a few other abilities. This allows them to learn as a human does (as opposed to the way they develop pretenses), as well as teach apprentices while the magus is doing something else.
Although that also gets to the question of what a pretense in teaching would mean... or organization lore for an initiatory tradition... faeries who could initiate magi would get massive vitality from sending them on quests...