How often does gog do giveaways? Like free games or random gamekeys in giveaways?

Yes.

There's usually one for each big sale, or two for longer ones (like the current Winter sale, which has given away Full Throttle and SOMA).

Sometimes when a new game is released, there is also a giveaway (usually a previous entry of the series, or a game by the same developer/publisher). But that's probably up to the publisher and harder to predict.

And then there are special sporadical events, like "you have received a free game game from your wishlist".

Not to mention the permanently free games in the catalogue.

Frankly, the freebies alone can keep you busy for a really long time. :)