Can I create a giveaway of game I have on the steam library that i didnt installed?

And how can you even gift that game?

No lol , it's in your inventory you must BUY game so you can gift it to some1 or give him a game key

no

No. Even though it's not installed, it's still tied to your account. You can only giveaway games you have in your inventory.

If you buy the game again, yes.

go read the FAQ

I think that someone didn't read some steam update - new rules. :D
You can't sell or trade the games that were added to your game library (subscription mode)

This is your library. You can not give away games from here, regardless of whether they are installed or not.
This is your inventory. You can give away games from here, via the trade or gifting system.