The Engineers missed their mission date 2000 years ago, when human technology was not very advanced. He's awakened, on a military base, on his ship, by an intruding force obviously of a technology far advanced from the one he was getting ready to go wipe out on Earth at the start of the common era.
A military man's only prudent action would be to strike first in an attempt to neutralize the alien, in this case human, threat.
I don't think so. Contrary to popular belief its better to think first. Assess your situation, then come up with a plan. I know it makes for boring movies, but its how you do things in RL. If it was me woken from a deep sleep in a military base, my first instinct would be to ask questions.