New Steam gift policy

ya it was possible

you need to buy it as soon as the winner has befriended you

you gift it to someone who gets VAC banned, you won't be able to buy this game as a gift on Steam anymore EVER

Please elaborate...

You can provide the winner with a key, you purchased on a 3rd party website (Humblebundle, ...). There is a option to enter a key, when you create a giveaway.

Depends on the game. I suggest you use http://www.allkeyshop.com/ to look for the cheapest price for a key of the game. Just a word of advice: G2A and Kinguin are market places where normal people, like me and you, sell their keys so there can also be scammers, just like on eBay.

It's not recent, it's almost a year old change.
You can buy a key from any third party store, steam is a bad option now days, because you can't send a gift if the store price on the receiver end is more then 10% lower.

The "recent" change happened in 2017 May, we know about it. You can only buy the game to someone who's on your friendlist
so you need to wait the GA to end, friend the winner, wait them to accept and then you can buy the gift if you two's regional prices doesn't have too much difference :D it's sooooo much simpler to gift from Steam /s