Is it possible to kill the running apps (SMS, browser, games ...) automatically by turn off the screen or during a certain period of time? My device is not rooted.
I'd use Greenify for something like this. It doesn't kill all running apps (as this is counterproductive to Android itself for many reasons), but you can select apps for Greenify to hibernate each time you turn the screen off.
For me this was nice because there were several apps like random game that would run all the time, and Greenify helps this.
Also, where Greenify used to be root-only, it
now works in non-root mode, (need to be enabled in experimental features setting, Android 4.1+ required). If you have secure key-guard enabled, try "Hibernate and Lock Screen" shortcut or "Pull up" gesture on Home soft-key. - Greenify description from Play store app page