Can you create giveaways using this method?

Yes

Just be careful with the region restrictions on gifting games via Steam.

Note. You have to be friends with someone for 3 days before you can send them a gift. A winner should not care about this as its only 3 days and not anything to do with you. I think you can buy for a friend right away and then just hang onto it for the wait period but I'm not sure.

That's exactly what gift means so yes. You can buy keys from legit resellers like Humble or Fanatic etc

While Steam does not sell keys there are countless sites that do. Have a look on ITAD or GGDeals for stores.

Buying and gifting on Steam is fraught with issues. There are no region restrictions, per se, on Steam, but you cannot gift to someone where the game cost in their region is more that 10% what you pay for it. In addition, if you repeatedly add random people and gift to them, Steam will flag you as a trader and prevent you from gifting any more. Also, if you are hoping to benefit from a Steam sale, you have to keep in mind that the winner has up to 7 days to respond, so there is a chance the sale ends before you can gift the game, in which case you would be paying full price.

Which is why most people giveaway keys.

Small precision: It happens that a person says "Thanks" exactly at the end of a giveaway and sometimes it is easy to confuse this person with the winner. So be sure to click on "Winners" in the left column of your giveaway's page to find the real winner.

Assuming you are from Europe, you probably can gift to all other countries except a few ones, most likely Isreal, Japan, Australia and New Zealand.

If you are really trying to make steam gift GA then it is best to look at game's steamdb.info price page before creating the GA. That will help you to restrict countries which can't accept game from your region.
For example let's look at Cyberpunk 2077's steamdb page. Based on not more expensive by 10% rule you will be able to gift game to everyone except those users who are from Isreal(expensive by 15.27%) and Japan(expensive by 20.69%)

These may also help you.
EU example
Malaysian example