1st problem: Set the sound to play when enemies hp its equal to 0 instead of when destroyed. This way the sound will play only when you kill them and not when Construct does.
2nd problem: If you are using a global variable to check how many lives the player has, make sure to give him new lifes when you hit the new game button.
3rd problem: We would need to see your setup. Post a capx or describe exactly how it works here.