I find both Gog and Steam very interesting and I saw that you can even sync your games so that you can play DRM-free as well as on Steam. I would like to buy Starbound on Gog and I saw that it was a game available on Gog connect, so if I buy Starbound here, would I be able to play it on my Steam account too?

Currently there are no games available on GOG Connect, it's not a permanent thing, they add games every once in a while, when publishers allow them to.

Also, it works the other way around: if you own a game on Steam and that same game is on GOG Connect, you can redeem it on GOG. If you have a game on GOG it's not eligible to be redeemed on Steam.

No. GOG connect works the other way round. if you have a game on Steam you can also get it on GOG for free.

However, the offers are time limited promotions since the publishers also have to agree to this. If the game isn't on GOG connect right now you can't get it for free here.

In other words, GOG connect is basically a marketing tool to get Steam customers to try out GOG's service.

There's a pretty thorough FAQ on the Connect page. It should answer most of your questions about the GOG Connect program. :)

Thanks for your answers, I have to say I'm a little disappointed but thanks anyways! :)