Q: Apps won't be killed

That's an extremely odd occurrence.  Once an app has been closed out properly, it should not launch again without user control

Make a backup.  Restore the device as new.  Test it again.  If issue persists, get the device serviced/replaced by Apple.

Which Apps?

How are you "killing" the Apps?

How are you determining that they are running in the background?

Please note that very few Apps run in the background.

You may want to start by reading this article:

Understand multitasking and background activity on your iPhone, iPad, or iPod touch - Apple Support

"Killing" apps rarely solves a battery problem unless there was something wrong with the app.

See this article for Apple's advice on maximizing battery life:

https://www.apple.com/batteries/maximizing-performance/

Things that will have a noticeable impact on battery life are location services and Background App Refresh.

Best of luck