how to buy a key

you can't buy a key directly from steam. You have to buy it from resellers, like fanatical, humblebundle, etc

But what you can do on steam is "gift a game". So you can make a giveaway on steamgifts and say that you will gift the winner the game from steam. There are a few caveats however, for instance you can only gift games to people if the game costs almost the same in their region than yours. (which means it's better to lock your gift on steamgifts to your region to avoid any problems)

You can't.

You can buy the game as a "gift" and then when you create the giveaway you mention that it's a gift and the winner needs to accept your friend request in order to receive the game.

you cant buy keys from steam... if you want to use steam for a giveaway, you have to create a giveaway for the game you want to gift, add the winner to your friendlist and buy the game after at the end as a gift. this means, the price could already changed. also if the winner dont accepts the gift (for what reason), you might end with an unsend win or would need to buy for probably higher price again...