You get booted from cover if you use the Lancer's melee ability, and you can kick an enemy out with the right action card. You may get equipment even while in cover, it says on page 14;
After a COG figure finishes moving for the turn, the player may place his figure into a cover space in his area. Moving into cover is free and does not reduce the number of areas the figure is able to move. Moving out of cover is also free, and happens at the start of a figure's movement.
For a more in depth set of answers, check here.
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