The 4 perks I've highlighted in Red, what is it called? Is it the battle order? Also how is it lost? I've sometimes kept this at 2/4 or 4/4 perks for several lives and sometimes lost it straight away. What affects its duration?
This called
battlefield-4
Best Answer
Those are your "Field Upgrades" you can unlock and earn many different upgrades which you can switch out like a kit. Each one has 4 levels of perks that they give. Each bar is a new perk. As you fill up your bar, you unlock more perks. You'll see in that screenshot they have unlocked 1 of 4 of their perks currently.
Your best bet is to choose perks that align with your play style and stick to your squad. By getting squad points you unlock them all pretty fast in a game. Also you should always have (preferably your squad leader) in the back where they likely will not be killed. Your squad leader should also make sure they are issuing orders on points to get tons of bonus points.
The possible Field Upgrades are:
All taken from here where you can also get more information!