Gifts and suspended users

I've never had this come up before, but my opinion is if you sent it before he got suspended it is his game mostly because now you don't know if the key is any good.

If I got that right, the answer to your first question is "yes". But take this into consideration: did you send the key through Steamgifts? If so, there's no way to know if he's already accessed it or not, but there's a chance. You could "unsend" the key, request a reroll and take the chances if you wish. I did it once with a cheap game. I took the chance, and it was still unused. If it was used, I had a backup copy to give to the new winner.

You are not required to provide a suspended user with a win. You can request, and are guaranteed to receive a reroll.
A suspended user cannot access won keys- the only section of the site you can see while suspended is the support page.
As such, if it was sent after their suspension began, you can be assured it hasn't been used.

If you sent it prior to the suspension, it's a bit of a crapshoot. I'd put in a support request for more information on how to best go about approaching it.

Well I had a winner who was suspended for a month, one day after winning my giveaway. Since I sent the gift through email, all I could do was wait it out.
If you are in no rush to give away that game, you could wait. Saves the support for dealing with one more ticket if things turn out ok.

If there is a chance he has already seen the key:

1. Contact him on Steam and ask him if he received the game.
2. If he says he has not seen the key yet, reroll.
3. If he says he did receive it but cannot mark as Received yet, wait until his suspension is over or until the giveaway is 1 week old to request manual feedback change.

In addition to what others have said, one way to check to see if he's used the key yet is to check his Steam games list to see if he owns the game. ;)

It's up to you, really. The rules state that you have the right to re-roll the winner if the winner is currently under suspension.
I'm personally against this kind of bonus punishment unless the giveaway in question was part of some rule violation itself. You can judge (with whatever limited knowledge you have about the person in question) whether you think the suspended person deserves to lose out on an additional giveaway.
When I was originally suspended for not activating some keys when I first started using this site, the unactivated keys in question were still on my Won page, but I couldn't access them to activate them because I was suspended, and so I was forced to buy new ones, and during my suspension period the majority of those keys were also rerolled so I couldn't even use them after I was unsuspended (including several wins I hadn't even had the chance to activate yet, and which were unrelated to my suspension). So I do carry some personal bias for these kinds of situations.

Thank you all for your input. It was helpful and enlightening. I have tried to contact him on steam already and I shall go from there.
Thanks again and have a great day. Cheers!