An item is allowed to have additional magics added to it, where the cost of the addition is the cost of the final product minus its current value. That is, take a +1 quarterstaff (2300 gp) and make it a +2 quarterstaff (8300 gp) for 6000 gp. See Creating Magic Items – Adding New Abilities:
Adding New Abilities
A creator can add new magical abilities to a magic item with no restrictions. The cost to do this is the same as if the item was not magical. Thus, a +1 longsword can be made into a +2 vorpal longsword, with the cost to create it being equal to that of a +2 vorpal sword minus the cost of a +1 sword.
If the item is one that occupies a specific place on a character’s body the cost of adding any additional ability to that item increases by 50%. For example, if a character adds the power to confer invisibility to her ring of protection +2, the cost of adding this ability is the same as for creating a ring of invisibility multiplied by 1.5.
For many items, combining functions (rather than upgrading them as with weapons) in one item carries a price premium equal in value to half the value of any functions after the first. This would also be part of the cost of adding magic to an already-magic item.
Stuff like directly using hides or medusa heads to make items, kind of. By default, yes, your character needs to have the appropriate materials (whose worth equals the crafting cost of the item), but what the “appropriate materials” are is left undefined and up to the DM.
Thus a DM may decide that a spike, gem, etc. is worth a certain amount towards the crafting cost of the item (e.g. that sword costs 2000 gp to make, but the gem you just found can be used for a part of it: you only need to provide materials [steel, leather, whatever] worth 1000 for the remainder of the sword). Most of the time, though, it’s more like “I go to the blacksmith and buy whatever I need for the sword from him.” Requiring specific, especially rare, materials doesn’t really occur in the rules except sometimes for certain spells (e.g. raise dead requires diamond dust).
I haven’t personally seen one, but I’d be surprised if no one’s drawn up lists of explicit materials for particular items. I doubt it’s official, though.
Do its bonus stack with Aid Another's not-circumstancial bonus ?
Yes. They are bonuses of different types, and therefore stack. Untyped bonuses always stack with all sorts of typed bonuses, and also with most other sorts of untyped bonuses (the exception being that a bonus will not usually stack with itself if you would be entitled to it more than once, even if the bonus is untyped; this is known as the Same Source limitation). They could have made it an exception if they wanted by explicitly saying it does not stack with Aid Another, but that would be pointless. Thus someone using Aid Another while having the feat effectively doubles the bonus that they offer.
What does mean "your assistance doubles the gp value of items that can be crafted each day” ? Do you craft twice faster (thanks to a very twister way of reading "double the gp value you can craft each day") ?
That’s precisely what it means. Actually, you craft a little more than twice faster because you are hitting a higher DC thanks to the feat’s +2 circumstance bonus, but that particular line doubles your speed compared to if that line was not there. Your progress on any crafted item is measured in silver; when the silver value of your work crafting the item is equal to the value of the item in silver, you are done. If your crafting checks produce twice as much silvers’ worth of progress, then you will meet the item’s value in half the time.
Why is Cooperative Crafting a feat?
A good question; to my mind it’s not very good design. Aid Another was already sufficient, I think, to model someone helping you out. If anything, I would have made this sort of bonus contingent on hitting higher DCs with your Aid Another roll (since, as you say, DC 10 is remarkably easy to hit), and for having both people have the relevant feat. This seems like an unnecessary feat tax to me, even if the effect is reasonably good.
On the other hand, I’m not too familiar with Pathfinder’s options in this regard, but if there are enough effects out there that stack and reduce crafting times or crafting costs, that can lead to very overpowered characters if they can get them all (see 3.5’s Artificer). Which makes me leery of an effect that doubles crafting speed, particularly when you don’t need to take the feat yourself; a cohort could take it, you could hire an NPC who has it, or whatever. Alone, this feat is fairly week. In combination with other, similar feats, it might be overpowered. Which again would just lead me to wanting to have a lesser effect, achieved just by hitting higher DCs than 10 on Aid Another.
Best Answer
It depends on the end product. It is essentially comprised of multiple products; a lens and a harness to hold the lens.
The Lens
The Harness
You can of course, combine these as you want. For example; imagine a gem inside a metallic frame held onto the face by a leather band, or a glass lens inside a metallic half-helmet.
The magical part could be the entire item itself, or it could be just the lens (glass or gem) either way, part or all of this must be crafted / finished using craft wondrous item.