Vader didn’t kill Needa. He choked him into a swoon, had him demoted, then reassigned. Vader’s evil, but he has a sense of honour, and he wouldn’t straight up murder a competent officer who’d own up to their failure and offer a genuine apology. Ozzel, on the other hand … you can tell that incompetent boob brown-nosed his way to the top and Vader’s had bad blood with him for a long time.
Stormtrooper armour is far more effective than the films let on. The stormtroopers we see get shot and presume killed? In most cases, they’re only knocked senseless; after a couple minutes, they shake it off and get back up.