What skills could a mundane teach a magi? For that matter: what mundane skills WOULD a magi want to learn from a mundane?
It might be easier to list skills a mundane couldn't teach a magus - eg Magic Theory, Parma magica, etc
But for mundane skills Artes Liberales is tasty, Verditus magi need to be craft masters, Flambeau tend to like martial skills to complement their magical, and Jerbitons are all about art and fitting into mundane society, etc
So really, you can probably find a mage wanting to learn whichever particular skill you have a Great Teacher for.
I don't see any reason why a mundane couldn't teach Magic Theory. It doesn't require the Gift, or indeed any aptitude for magic at all, it's pure theory. Indeed in my saga the covenant's (non-magical) librarian has learned enough Magic Theory that she has been holding a season's teaching in the last couple of years for the magi, their familiars and interested bystanders. These lessons worked a lot better once one of the magi remembered to extend his Parma Magica over her.
It's much less likely that a mundane would be able to acquire Finesse, Penetration or Parma Magica, but that's more a matter of access and utility than actual prohibition.
It depends on the mage - a debater would want to learn skills like Folk Ken, Intrigue and Artes Liberales to do better, a warrior mage would want weapons teaching, and a Verditius (or other crafting mage) would want to learn mundane crafts in order to make better items.
A min-maxed mundane teacher companion is worth their weight in gold for the number crunching grognards out there. Puissant and affinity with teaching, communication 5, good teacher, getting a 30 XP season is possible.
Farm out the early teaching seasons of an apprentice to the Companion. Latin, Artes Liberales, Magic Theory. In 1 season the mundane teacher is doing what the magi could do in 2 seasons. Once the basics is over, the mundane teacher gets the magi to teaching 3 in a season, making the apprentices art scores a lot better in the long run.
Concentration can be taught by a mundane.
Give the teacher a longevity potion, and arguably could have magic theory of 7+ and keep teaching some more established magi. Especially with affinity for magic theory.
The teacher could have a smattering of 3s in lore skill, leadership, intrigue, etiquette, to flesh out a magi.
Even things like athletics and swim. Magic can do a lot, but how good is the magi at casting when drowning? The magi could vaporise the grumpy townsfolk, however, that has long term consequences. Athletics 3 makes running, and thus not looking like a mage, an option.
I've presented the munchkin teacher. Even a less min-maxed mundane teacher is a huge boon.
I don't have my books on me at the momemt, but when a mage extends their Parma Magica to cover someone else, does the someone else have to be Gifted in order to benefit from the dampening of the Gift penalty?
Teacing, being a social interaction, should be affected by a Gifted student, no?
If you are protected by Parma (this includes a magi extending his Parma to you) you are not affected by the negative side of other people's gift. If you are gifted or not has no impact. However, remember that if you are gifted, this doesn't stop you from affecting other people.
Yes, teaching is a social interaction and is affected by the gift (including the -3 penalty to social rolls and totals).
Unless the Magi has taken an apprentice before, most Magi do not have Teaching. So having a mundane teach a Magi how to teach, is a great benefit, for both Magi and his apprentice.
My PC magus sought out a teacher to learn ropemaking fifteen years after his gauntlet.
Mundane teachers are probably the best source to learn the Academic abilities, as well as languages. They are also great for learning various Area Lores.
And martial too, especially for a mage of the school of Ramius.
The most common situations I've seen(discussed or enacted around our table): martial skills from the Turb captain, Leadership from the Turb captain. Teaching, Artes, Philosophae from a scholar.
My table also discussed Profession Sailor (we travelled by boat a lot) and craft skills (to reduce finesse penalties), and Medicine, but not very seriously.
From Japan:tea ceremony & kabuki theatre?