Says Forge already exixsts in my acc but i don't own it!

You need to wait until it no longer thinks you have Forge, unfortunately.

Same here! It's very frustrating :-(

Try to re-log and then resyncing the account.

You should sync your account in the middle of the week, that way these weekend things won't get in the way.

Free weekends.

Sync your account mid-week and it will reduce the chance of this happening. Now it is in your recently played games list though, you'll need to wait 2 weeks for Steam to remove it and the sync again with SG.

No it will be about 2 weeks until you can enter Forge giveaways. Your steam activity will still show that you have "recently played" the game. SO the system thinks that you own the game. No way around it from what I understand.

Use the search bar. Many people have complained about this issue already, and you could have found the answer there.

So you played it while it was on Free-Weekend? Just have to wait till its over, and then, a few hours later, it will be removed from ur library. Thats all u can do, wait!