A lot of your questions are answered in the patch notes, but I'll give it a shot:

1.) Yep! You can be in a DF group and you'll be matched up with other DF groups. A DF group can't be matched up with a premade, though.
2.) Uhhhh I don't remember that being a thing and I don't think it would make much sense.
3.) Yep! Though, it is hard to tell just based on gear ilvl requirement. For example, Titan Extreme might be harder than Ifrit Extreme, but Ifrit EX requires a higher gear ilvl. Also based on gear ilvl alone, Ultima is harder than Titan HM.
4.) There's a quest chain for a new ilvl 90 weapon, whether that's a new Relic or not remains to be a mystery.
5.) Probably not, but couldn't tell you for sure.
6.) You can only get 1 bonus from each category a day, iirc.
7.) No idea on this one.
8.) Yep!
9.) I think there's a lockout for 40 minutes on using the kick feature, so you can't repeatedly kick people over and over from the instance. You can also report any abuse of it and it'll be handled by SE.
10.) Yep, I think it's actually in the notes what new items you can store in the armoire.
11.) No idea on this one either.