Can I still buy games from steam and do giveaway?

Yes, though sales might be bad do to timing and also if you are in low price region you can't give to higher one.

Of course you can buy games as a gift on steam but as far as I know that only works for the same region or regions where the game costs less till max 10 % more than the price is for you region. Check SteamDB for price info. If you wanna buy a game with a coupon or from a deal/sale an other problem can be that the winner has 7 days to accept his win.

Two of the biggest official sellers apart from steam (that sell steamkeys) would be Fanatical and HumbleBundle