Not to be super anal or anything, but this is Mission 2-3, _not_ Mission 6. Yes, it can be your 6th mission, but that is not what it is called.
By handing crystals to the conquest guards, you can skip Mission 2-2 for sure, and I believe a few others as well.
Once you get your country's Mission
False... the chest keys are all Rare/Exclusive.
This means that you can have one of each at a given time - on your person, in mog house, or in storage. This is the case of all RA/EX items... Ex meaning it can't be traded or sold normally (sometimes to NPCs), RA meaning you can only have one at on
No, it's not used in the recipe, but it is required to have in order to synth the recipe.
I think Pikko's comment is just saying that the easiest way to signify that you need the skill in order to craft the item (without rewriting a bunch of the database code for the site) is to add it to the rec