I had a steam version of the game and I have just bought the DLC pack on the official site.
But it seems that they are not usable since after I installed all 4 DLCs nothing new shows up ingame.
Is there any problem with the installer or I need to do something with steam?
you just need to ensure that you install the DLC into wherever steam has put the game. It has no idea where the game is, so it guesses, so you need to browse to the steamapps/gratuitous space battles folder and make it go there instead.