Xbox – How to change the zoom level of the HUD map in BF3 on xbox360

On the XBOX 360, open the parachute by pressing "a". You must be past a certain height threshold for your parachute to be deployable. A double press may be required to open your parachute.

Source: http://www.battlefield3gamer.com/apps/blog/show/9807786-how-to-open-parachute-in-battlefield-3

You must press and hold your reload key (default R on PC) to pick up any placed (or dropped items) this includes T-UGS, and most gadgets from all classes which are not another held weapon.