1.) No

2.) Officially no, though when the Moonfire stuff came out and I was trying to get cloths, I never got any. It's been ages since I got a good ARR map drop, and while I don't do them like I used to because of the Voidrake trade-ins making them much less valuable, something does seem off.

3.) Yes, screenshot from a Lodestone comment for proof: http://i.imgur.com/q2Zdw9l.jpg

4.) They're a whole separate crafting material found on a different node than trillium and used for other things. Though yes, it is weird.