Xbox extras app is for avatar editing etc.
My question is "Can we buy apps/games using the Xbox live game score?"
No. Gamerscores are pretty much the same as the Trophy system in PSN. It's to determine your rank in gaming. In order to take full advantage, you have to register at Xbox Live Rewards. With the rewards system, you can gain MS Points. Although MSP are now discontinued, these are converted to local currency depending which country your account resides in, and they are deposited to your account which then you can use to make purchases.
Check out how Xbox Live Rewards use your Gamerscore details:
Xbox Live Rewards
Remember that XBL Rewards are not just for Xbox consoles, although mainly its offerings like 'how long have you been playing this game' requires you to have a console. Other than that, it also gathers your XBL activity from other services as well like Xbox Video on Windows 8.