About getting keys...

You can receive free keys from IndieGala challenge game or LootBoy, but in both sources that keys can be already used.

You can check if the person activated the game on his account via sgtools.

It does not matter where you get a key from, as long as it can be activated on Steam, you can give it away here. Beta keys that will only work temporarily are not allowed. I would also not recommend trading for keys or getting them from shady sites because it will make you look bad if you give the key away here and it does not work or if it gets revoked in the future because the person you got it from used a stolen credit card or other bad payment method to obtain it. There is no way for you to check if the key is valid before you create the giveaway.

Winners are required to activate all won games on their Steam account that is linked here. Technically, yes they can give it to someone else or activate it on another account, but they will eventually receive a suspension. If they continue to not activate wins and are suspended multiple times, they will eventually be permanently suspended for continuing to break the rules.

1st Question - Free Keys
It may take some time for the game to be added to the free list but as long as you are happy with your level not increasing it is fine. Some sites that occassionally giveaway free games are:

• HumbleBundle - last one I recall was Surviving Mars but that was mid last year ....
• Fanatical - example the recent 'Internet Cafe Simulator' game - Fanatical giveaway less freebies then Humble
• Twitch - there is a certain channel on twitch that you can "buy" games on for channel points (get those by watching the channel) ... check the "Where are those giveaways coming from?" topic in Deals forum for a hint (we can't link to it - against the rules).
• Alienware Arena / SteelSeries - both giveaway games every now and then ... however the giveaways are QUICK, keys go super fast due to bots, and a lot of giveaways can be non Steam or even beta keys, keep an eye out.
• Gleam - you won't find any links on SG due to the rules (you need to follow on Twitter, Facebook, etc.), but Gleam do a lot of giveaways. Keep an eye on Reddit forums, etc.

2nd Question - Won the Giveaway
Yes a person can grab the key and activate it on another account, their 2nd account or a friends account, however that is against the rules and if they mark it as Received that will likely get suspended for it (banned in some cases).