Forcing users to have their profile as public defeats the purpose of wanting to have it private.

People who want to post proof can redirect to their inventory, or post a picture of the game in the inventory, but its certainly not forced to anyone, and i dont see why either, since some people might buy the game when the giveaway is finished.

As far as waiting period, there is something similar, its a restriction on the amount of giveaways one can make.

If you dont like to see fake giveaways, just check their profile, how long have they been here and steam profile, thats something to consider when joining public giveaways.

The solution I think that would work best is one that's been suggested a few times:
Your giveaways until you reach $10 or so must be 'verified' by synching in the same way that your games list is synched every week or so. You can keep your profile private, but must have the game available in your inventory and synched before you are able to make that giveaway.

Anything that requires SteamGifts to force members to keep their inventory or profiles public will not be an option.

What about a good old warning only for people about to create their first giveaway? A 3-4 lines message right on top of the giveaway creation page telling you "hey, you're about to GIVE AWAY A GAME", two times, one in english and one (if you don't live in uk etc) in the language your geolocated ip is speaking.

Additional: the rest of the page obfuscated with some cool jquery script until you click or something. And "Mods can ask you to give a proof of the game in your inventory, or some pixelated image of the steam key" just to sound more intimidating even if you'll never ask.
Or expand the forum and/or give the whole set of rules a more prominent position. They're not really visible right now. I mean, I found the threads in the forum and the things I've read there were already kinda clear (apart from the formatting one, damn you formatting). But it's not like the others are so intelligent like you and me, you know (sarcasm intended).

I think an interesting idea would be to check giveaway history and mine how many people did giveaways in the same day that they entered the website, and how many of those were fakes. If we do this kind of statistical analysis, we may be able to reduce those fake and annoying giveaways by disallowing giveaways for new users for some small period of time.

Another thing we could do is to help translate the website or, at least, the process to create a giveaway.