How do you use those weapons and camos you get from battlepacks? Can't seem to find them.

You first need to unlock the weapon. Once you have acquired the weapon you will then need to hit the "customize" button and at the bottom their is an option for "visuals"

Are all the weapons from battlepacks purely aesthetic, or do they have stat values like weapon variants in cod?

They're only skins

I just got the doughboy bar.... pretty excited