go into your options menu and make sure advanced movement is turned on. Then hold control while you click. you will run, expending more energy but less time units. If you would have ran you would have been successful.
You can also "strafe" with control key. Sometimes comes in handy peeking around corners already in firing position without stepping out and then turning to fire.
Lesson learned... don't give rocket launchers to rookies
Not usually at first, but once I can get the plasma tank I usually grab one. When I grab them early I just seem to get them killed, and $450k a pop is a lot more costly than a couple $40k soldiers, especially early on in the game.
Proxys might be a good idea, I've never really used them, but they could definitely make the engine room encounters easier on me. I'm thinking it's probably a good time to start focusing on live captures too... time to dust off the stun rods!