Talisman attunement question

I have a dwarf Verditius mage.
Magic theory 10+2(pussiant)(enchanting items)=13
Philosophiae 8(enchanting items)=9
Metalworking 2+1(dwarf gets +1 to craft)=3
Stone cutting 3+1=4
I make an iron wand with Agate crystal on the top.
Agate 3 air 5 protection from storms 7 protection from venom
Iron 7 harm or repel faeries
Wand/Staff 2 repel things 3 project bolt or other missile 4 control things at a distance 4 destroy things at a distance
I want to make a talisman form it.
If I instill an spell for harm faeries from distance then I get 7+4+9(max 13)=13 +craft can be both but only one so i take stone cutting 4. 13+4=17 to the lab total, right?
Same season I can attune it to Air 3+9=12, right? So i can cast air spells while holding it with +12?
And I need 4 less vis cause crafting is 4, right?

You're quite close. The pre-errata language was vague so I understand the mistake, but you don't actually get four pawns of vis off of the cost of investing effects in the item; you get four pawns of Vim vis off when initially opening the item so that it can be enchanted or turned into a Talisman at all.

Other than that, you're 100% right.

I'm not at all certain that I understand your question. (I hope that Hammer 'n' Godsmite answered what you were asking)

Could you, without the numbers we can see those in the first post, give us what you're asking?

Are the calcutations right? Do I interpret the rules right?
Especially do I get the Philosophiae bonus for the attunemented talisman spell boosting effect too? That seems like kinda OP.
Another question can you attune the talisman till you take all the effects described above? So can I have all the 8 attunement if I instill one spell for 8 seasons?
Then I can yous all those bonuses if I cast appropriate spells?

Only the biggest talisman attunement bonus applies for casting a spell. You don't add them together. See ArM5 p.98, the first sentence of the last paragraph in the Talisman Attunement section.

Philosophiae also doesn't apply as an attunement bonus to spellcasting -- it only gives a bonus to the lab total when enchanting effects into the item.

So you would get +7 to spells to harm or repel faeries, +3 to air spells, etc. You would still only +7 to harm or repel faeries of the air.

Okay, thx.
One more question.
Who is considered a faerie?
Mythical creatures right? Its kinda vague.
Dwarfs, giants, satyrs, elfs, ork, gnone.. for sure.
But what about dragon? daemon?
Or who is considered definitely not faerie?

It's usually explicitly described for the individual creature, as Faerie is one of the realms. Unfortunately you can't exactly draw a line based on the type of creature it is. There are Faerie giants, and Magic giants. Most dragons are Magic (I think) but there are some Faerie. Dwarves, elves and gnomes are pretty explicitly Faerie. Demons are always Infernal, and not Fae.

There are four realms, plus the mundane realm, so if everything were divided evenly, you might expect 1/5 of the things you encounter to be Fae. It won't be, obviously.

Perhaps more relevantly to your question, your character is not a Faerie. Characters can be affiliated with any Realm (for example, the magi of the Order of Hermes are all affiliated with Magic) but your character being a "dwarf" is just them having dwarven blood in their lineage, not actually being a Faerie themselves.

A creature is only a Faerie, or part of any of the Realms for that matter, of it has a Might Score. In the main, core rulebook, there is no way to play a Faerie, though options for doing so exist in other books.

Speaking of which... The four Realms are Magic, Faerie, Divine, and Infernal. Each one has one "restriction" as to what it can represent: the Magic Realm is creatures who are more perfect and powerful versions of creatures, objects, spirits, and base matter like fire, air, etc.; the Faerie Realm's creatures are all literally the stuff of legend (basically, it only exists if someone somewhere has, at some point in time, spread stories of it as if it were real); Divine creatures are essentially angels; Infernal are demons. Aside from making sure you don't leave those extremely broad restrictions, anything goes; since "angel" and "demon" don't actually mean anything shape-wise, basically a situation arises where Magic is the most limited in scope by technicality but all of them are incredibly broad and most mythological creatures can be part of multiple Realms, including all of them.

Is a dragon a more perfect and powerful reptile? Yes, then it can be Magic. Do people tell legends of a dragon that isn't actually there to agree with the story? Poof, a Faerie Dragon. Would a draconic form help an agent of the Divine protect people against the Infernal and lead said people towards righteousness and faith? Yes, so a Divine dragon may or may not exist but certainly can. Could a draconic form do well to serve the opposite function for a demon, allowing it to harm people both directly and indirectly, or tempt them towards sin? Most certainly, so Infernal dragons may or may not exist but can.

Now, dragons are weird, because while the Divine Realm as a rule is stronger than any of the other Realms and consequently produces stronger creatures, dragons are the exception and are usually stronger when originating from the Magic Realm than from any others. But the idea stands that a dragon could be of any Realm. As well as a dog. Or an animated desk. Or a giant, or a ghost. The list goes on. Even creatures who can't be modelled by every Realm usually encompass more than one; Pagan gods are both Magic and Faerie, imps can be both Infernal and Faerie, so on so forth. (Though I can't think of a Magic creature who can't be emulated by the Faerie Realm... Hmph.)

Hope I helped.

Any and all things with a Faerie Might score.

As others have mentioned, multiple versions can exist, simulataneously.
Try taking a look at chapter 13 of ArM5 (that's p. 191ff), it even has as an example a supernatural wolf of each Realm.
There are published Giants from the Magic Realm (RoP: Magic), Faerie Realm (FoP: Faerie).
Nephilim (RoP: Divine) are large and grow larger, essentially qualifying as Divine giants, and there are certainly gigantic demons, of the Infernal Realm.
Of these, only those with Faerie Might would be considered faeries.

I'm not familiar with Divine dragons, but I am aware of published dragons associated with each of the other 3 Realms of Power (Faerie, Infernal, Magic).
While demons by definitions are associated with the Infernal Realm, some dark Faeries imitate demons and try feed on stories of temptations and sin, like leeches.

Anyone or anything without a might score.
Anyone or anything with a might score associated with one of the other 3 Realms of Power.