Why i can t make a Dota 2 give away?

Dont listen to him. You are just not trying hard enough!

No Solitaire?

Minesweeper?! Yes, please!

I have some spare copies of "Barkley, Shut Up and Jam: Gaiden"

Actually, I saw a guy with multiple copies of TF2 in his inventory a few weeks ago. AFAIK, activating one of them will still give you premium + the proof of purchase hat. (Same as getting the game via The Orange Box)

It used to be possible to gift this on SG, but people only made troll giveaways and none of them actually had the game to give so it was eventually removed.

no it's free.

The copy you got and the copy on Steam are not the same. ;)

Nope, the keys you've got are only for the free game. What's for sale on Steam is the starter pack with items.