a) How to put the application to work on background Long press menu button to see current running apps. Tap and hold the app you wish to keep running in background and drag it down. It should lock the app.
b) How to make the applications to start on background Go to Settings -> Power manager -> Background app management and you will get a list of all the apps that auto start. Assure that Should I Answer is on, this will also prevent the system from killing the app when the screen is locked (turned off).