As I said, noted are......(see previous post). There may be an Army but they have yet to be mentioned in any official publications.
Who knows.....
A little of column A and a little of column B. As I see it, there are factions (I don't see an actual central authority among the Anti-UN but I don't seem them as just terrorists cells since they have a distinct military discpline surrounding them). In the Americas, they are probably dealing with guerillas (like the ones in Guatamala back in the day). In the Pacific/Atlantic and in Eurasia (and perhaps Australia), the UN is probably facing a much more organized group. I can't really make out the situation in the Middle East/Africa.
This is conjecture, of course. The basis for this answer is from scenes in M0 and the Compendium.