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Yes for the first, no for the second (although that is in debate as shown above)
Nothing suggests that you ever need a formula for more than what is printed in the book though in my readings. For instance, the argument is that you would need a formula for each level of scroll (for spells) or a formula for each level of wand, but not for each spell.
Same deal here with the special material items. You need a formula to craft it at low grade tier, and a formula to craft it at standard and then again at high grade. But not one per weapon.
The way I see it is, you already have knowledge to create the weapon from the basic crafter's book or its own formula, the cold iron formula is just knowing how to work with the material with weapons and the standard grade cold iron formula is a more refined version of that same knowledge allowing you to better utilise the material in more elaborately crafted weapons.
@Cordel Kinter
While the price isn't prohibitively expensive, if you are restricted by settlement level and cannot purchase the formula (a city like Kintargo is only level 7 for instance) then it can be quite painful for a crafter to have to use inventor for every single weapon they want to upgrade if they are doing it across 3-4 members of a party with a special material, on top of runes and such. 4 days each to invent, 4 days each to craft, 4 days per rune you don't have the formula for so you can transfer them, 1 day per rune to transfer.
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Yes, and Yes.
I do not agree with TGG. There is no such thing as a "Generic Cold Iron" Formula that empowers you to use that material for any Weapon/Armor/Object that you can otherwise craft and you'll also need a new Formula for each different tier of Special Material. You need a Formula for a Low-Grade Cold Iron Dagger, a different one for a Standard-Grade Cold Iron Dagger, and a different one for a Low-Grade Cold Iron Rapier.
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I agree with The Gleeful Grognard.
Or else would be nearly impossible either to provide to the party or have to always rely on NPC ( which for some magic reason would be always able to craft what you need ).
"We find some cold iron which is known to be lethal to fiends. Now we can make weapons out of it and storm their evil lair!"
"Excellent! I Need a greatsword"
"Rapier here!"
"Starknife dagger"
"Gnome Flickmage"
"Wtf is a flickmace? I don't know how to make your weapon"*Several months later*
Ok we are done!
Unfortunately, the fiends already conquered the world.
The time consuming part isn't the recipes, it's the crafting. Even if you had every recipe it would still take months to make everyone in the party a weapon. It's always more time efficient to purchase something that has already been made, rather than the party making it themselves.
This is why you need a recipe for each individual item. You could spend only 4 days per item if you wanted to pay full price, but at that point why not just buy it? The only reason I can see is if the item isn't available. The problem with that is Cold Iron and Silver are common materials, so that's unlikely to happen.
Further evidence of this interpretation:
The reason it's different per item is because the special material has a different forging process for each item. Just because you can make a dagger and a bastard sword, doesn't mean making them both with adamantine is the same process.
'I won't ever forget when I met a gnome flickmage. We were in the Holy Wood, see ... '
I honestly don't *like* the interpretation of 'one formula for each weapon', but it has the scenario support that Cordell Kintner mentioned above (formulae are separate for adamantine shields and bucklers). That said, I'd probably be somewhat lenient. I don't think long-, bastard-, and greatswords are different enough to require different formulae for this purpose (using the reasonong someone else gave over forging methods), as an example.
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Yup, in PFS its definitely one formula per item x precious material combo.
In a home game I'm planning to make a "Principles of Cold Iron Weaponry" type manual, probably costed at about 5-10x the level appropriate formula but covers all weaponry, you must still have the formula for the base item. Ditto for Armor (shields will count as armor for that purpose and that purpose only). Its a bit handwavy, of course, but basically viewing the the idea of there being somewhat-overlapping, but distinct techniques for working with the special material when its comes to working it into sharpenable shapes/affixing to hafts/etc versus shaping in durable armor. Of course that home game is set in a emerging from a dark ages type thing, so this types of books are lost treasures. Most existing precious material items would be magical, 'legendary' pieces (even if only a +1), a large percentage would be relics (GMG style), etc. One of the themes I'm still working through is 'what happens if the PCs share this newfound knowledge/keep it for themselves, etc'
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Pathfinder society having single item formulas in no way invalidates anything I said before.
You can have a formula for "wand of fireball level 3" that isn't a formula for a level 3 wand. Both can exist within the same system. One wand is a formula for a wand that only accepts fireball as a level 3 spell, the other wand is a formula that accepts all 3rd level spells cast during its creation.
I am just saying that AS WRITTEN in the crb, nothing suggests that you aren't simply buying a formula for all cold iron weapons of a grade when you pick up a cold iron weapon formula.
You can argue RAI, in which case I would again direct people towards the scroll and wand crafting sections where it is quite clear that RAW you don't need a formula per spell with how it outlines the crafting process, just per spell level.
Wand
For the most part, the process to Craft a wand is like that to Craft any other magic item. When you begin the crafting process, choose a spell to put into the wand. You have to either cast that spell during the process, or someone else must do so in your presence.
Scroll
The process to Craft a scroll is much like that to Craft any other magic item. When you begin the crafting process, choose a spell to put into the scroll. You have to either Cast that Spell during the crafting process, or someone else must do so in your presence.
Don't get me wrong, I am not saying that a person doesn't need to know how to make a longsword at all, they would still need that basic knowledge. But that is where the basic crafters book comes in.
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Wands and Scrolls are different; they are receptacles for a spell. You make the item, cast the spell into them, and they store it. They are akin to Runestones. You wouldn't have to make a different runestone for every rune, so why make a different scroll or wand for every spell?
Meanwhile, making an Axe vs Sword require very different smiting techniques, and knowledge on how to manipulate special materials in a way that will fit with that weapon. Sure you know how to make a sword but you also need to know how to work cold iron in a way to make something that functions in the same way. Cold Iron is iron that hasn't been heated up to shape. It's smithed cold, which is harder and requires special methods for each weapon, just how each weapon has their own methods of creation. You can't just add the material to the metal soup and call it a day.