Adventuring Fellow Items Questions

I noticed that you can get a Chef's Hat for your Adventuring Fellow with AF points. With this equipped on your AF, you (obviously) get +1 to your cooking skill. But, by having this equipped on your AF, does it preclude you from having it on yourself, the one you bought with guild points? It is a R/E item, which is why I ask. Though, it seems pretty assumable that your inventory is completely separate from your AF's.

Also, I'm confused about the Chocobo Wand too. There seems to be very little information on it. It is listed as an "item for fellow" on the wiki, but it says that it extends chocobo riding time and can be stored in item depository. So, it makes it seem like an item you can use on yourself, not your fellow, to grant you the 30 mins of extra riding time. Can anybody confirm that?

Sorry if these are dumb questions; just trying to understand clearly!

You dont equip your own hat on your NPC, you just buy one with the npc points at guy in jeuno. I doubt that your npc's chefs hat will gratn you the cooking bonus though. Its just for the looks and nothing more, I'm sure I've read it somewhere here ==>> http://wiki.ffxiclopedia.org/wiki/Fellow

Anything you equip or your NPC is for them only, The chef hat is for looks same as all the other gimmicky items any additional effects become void.

That's pretty lame and deceptive.