How do i know if the winner of my giveaway has seen the code?

And you thought that'd be a good idea? You're not supposed to do that... O_o
You really need to read the faq and the guidelines asap.

Only enter to win games you do not already own, and do not enter to win DLC if you are missing the required base game.

That little tidbit was taken from the guidelines. And yeah, regifting games you've won here is not allowed.

The site can't detect it, due to issues with Steam's API. Steam has two versions of the API- one that users log into, which gives that user access to their library information, and one that developers/websites use, which can only access public information. For whatever reason, DLC ownership isn't considered public information, so SG doesn't get the information for- and thus can't determine- ownership of anything which contains at least one DLC.

Thus, it's important to manually check anything with a DLC [ie, anything ranging from individual DLCs to Complete Editions] before entering. Clicking the eye icon next to the giveaway or at the top of the giveaway's page will allow you to hide the game from future results (unless you toggle that function off in your account settings). Note, however, that the entry button on the giveaway won't be blocked, so you still need to be careful if you're accessing a giveaway from anywhere other than the search results page.

Also note that the API doesn't send ownership information for games that've been removed from Steam, games that are Profile Features Limited or that've been released within the past 24 hours, or games that're misconfigured by their publisher. Basically, even though DLCs are your main source of issue, it's a good idea to confirm ownership- if not before entering, then certainly before accepting the win.

In the end, the only time you can really rely on the site to block participate on owned content, is when you won that content from the site- and that's just because the site doesn't need the wonky API to check locally accessible data.

In any case, you've put yourself in a slightly awkward situation. If you hadn't owned the game, and had simply passed it on, then you could have fixed that by getting the GA creator's permission to have their giveaway deleted, or by finding and activating another copy of that game to activate. But since you already owned the game, that would technically fall under "Misuse of Giveaway Feedback"- which warrants an indefinite suspension. I thoroughly doubt staff'd go that far on the matter given the circumstances [though I've seen it plenty of times when it was intentionally done within groups to exploit CV] but, well, it's still something you should probably get run by staff asap to be safe.

That said, I wouldn't worry too much- as noted, the main aim is to have the game activated on your account and, given that the nuance of when you activate a game to your account doesn't matter much if you're not actually exploiting any CV, you're fundamentally in the clear already.

Well, if we were trying to resolve it smoothly then, given the circumstances, the cleanest solution'd likely be to just have your created giveaway deleted, thus setting things back to sum 0. Ultimately, however, staff'd be the ones to determine how things'd need to progress. As-is, it's likely enough they'd simply let things sit and just caution you to be more careful in the future. Basically, you probably just wanna be careful not to do this in the future with any CV-granting game, and in a manner that seems intentional.

Then the right thing to do is tell the ga creator you already own the game and ask him to re-roll.
Not only you entered a ga for a game you already own, but you accepted and re-gifted it. Not very honest.

For future reference, most elements on the site [eg, the asterixes in question] give more information when hovered over.