Once Cole beats all the guys in the big room with the turrets, all you have to do is run straight at the turrets until you hit the gate. Then just aim up and shoot the turrets until the blow up. The turrets can't shoot back because they can't rotate far enough to aim at you.
In the stage Life or Death, there is a small key on a dead soldier in one of the lifts where Cole starts the stage. Grab it to open the small lockers in the stage. One of the small lockers in the first power conduit pit has a databank item that upgrades the alien grenade (it now homes in on enemies).