I'm glad you're enjoying the game so much. I still remember when I first started and how much I binge played the hell out of this, I'm close to 600 hours played total right now.
The double xp weekends seems part of the Final Stand for free promotion they have going (they will eventually give all the DLC away for free from here until BF1 comes out). You can check news about the game at:
http://battlelog.battlefield.com/bf4/news/.
The Battlepacks, I think you unlock 1 for each class service star you get and they've basically been randomly giving them away for free for years now, usually part of some community mission or promotion, or maybe they just give out a bunch to new players when they start.
I don't actually remember if the game has AA emplacements like the one you mention. I think the Final Stand maps do have some that can be effective against vehicles, one of those futuristic weapons I think.
Divisions is all based on how you rank compared to other players, so something like Commander which might no be super popular will probably take a much smaller score to get to Division 1, than something like the Assault class. You can check how your different stats compare to other peoples in more detail here:
http://bf4stats.com/