Welcome to the forums.
Android works differently than say windows. Apps are opened in Android and put into memory for faster access. The system will automatically kill a app if it needs the memory.
By manually killing apps, you are actually worsening your battery life instead of helping it. When you kill a app, it will either restart, or another app will open in its place. This constant tug-of-war will wear your battery down faster.
By turning off the auto synch and doing it manually, you can prevent your phone from constantly searching for any new messages.
Hope this helps.