I understand that there are specific battlepacks that you get for using guns. When do these battlepacks get unlocked? I assume it is after a certain number of kills?
Took me some fiddling but I found how to find your unlock progression for weapons. For some reason, the BF4 battlelog doesn't open this when you click on your weapon from the stats page (like it did in BF3).
To access the unlock progression of a weapon, click on soldier, then Unlocks. By default, this shows a page with all your unlocks like this:
After selecting a weapon, if you mouse over any attachment, it will tell you your progression in (X out of Y kills for the unlock). The orange bar helps too.
As for what is in the battlepacks, they are random attachments for the weapons + XP Boost from what I could see when I got them (same for my friends). The main difference from the levelling battlepacks is that the levelling battlepacks seems to give you attachments for random weapons from your inventory (even some you haven't unlocked yet).