For your barrels. Pick a barrel is the middle as a good refernace barrel and give it a name. Then make a trigger with the condition as this;
!(Alive BarrelName)
And the activation as this;
"1" ObjStatus "DONE"; obj1=true
This will tick off the first objective in your briefing, if you have one (change the number if this is not the first objective). And it will also set a variable which you can use in the base at the end.
With a trigger over tha base, group the players group with the trigger (F2), this gives you new options, make it group present and set it do condition;
This && obj1=true