First time doing giveaways, am I doing this right?

You don´t need to send a mail, but of course you can send also one...sometimes i do both, just for the fun :-)

If you provided a key on site when you were creating a giveaway - than everything is fine. Winner can access his key, he can activate it, he can mark giveaway as received.

It sends it automatically, but just to be sure it's best to also invoke the spirit of the goddess Hecate and sacrifice a newborn in return for her psychically sending the key to the winner. Or, you know, an email if you're not into the new-age stuff.

... is you avatar a demonic hello Kitty?