Does DLC Show in the Owned game list ?

On Steam? Almost never, no. Only soundtracks and some special DLC's

in most cases no. There are rare examples of DLCs having their own entry in library, like Borderlands campaigns, but tat is rather exception.

Only way to check if user owns DLC is having him in friend list - try to buy DLC as a gift sending directly through steam, and it will show if he owns it. Then cancel the purchase.

It does show up under the All Games tab, checked it on a friends profile (DLC for Skyrim and Fallout New Vegas). I don't know if it only shows if the person is on your friend list.

Okay thanks for help