1. How to get a background music in your game?

2. How to make doors first switch off (with the red light texture) and the on (with the green light) ?

Select any brush and press n. Scroll to the bottom of the top list and choose worldspawn. Enter a key 'music' and value is the path of the music you want within the pk3s.

It works, thanks. Can anyone solve my door problem?

try to deactivate it with a target_deactivate, it should take it to red

I haven't used this yet, but doesn't it have something to do with the 'locked' spawnflag?

EDIT: Yes, if you set the 'locked' spawnflag, the door starts off red, and turns green when 'used' by another object (NOT a player). This of course assumes you are using one of the standard door textures, although I believe one door has it's colours the wrong way round (i.e. green for locked and red for unlocked).