Hi, can I redeem codes (after purchase) directly to the steam? Or it's just a buy-download principle?

You don't get Steam codes from GOG, only DRM-free installers.

GOG.com doesn't sell Steam codes.

You can install the game and add it to your Steam library as a non-steam game, if you want.

Hey cool, Valve has a French Monk too!

It would certainly be nice if you could, but no you can't. If you buy a game from GOG you get it from GOG, just like if you buy a game from Steam you get it from Steam. If you could redeem your GOG games on Steam too then where to buy from would be a no-brainer, but as it stands you need to pick GOG or Steam based on their merits and what suits you.

GOG gives you:
- an installer which you can carry around in a USB stick if you want, and doesn't need an Internet connection to install
- better quality assurance - Steam leaves that up to the publishers
- extras, such as manuals, wallpapers and soundtracks

Steam gives you:
- automatic patching, which GOG currently lacks
- achievements, trading cards
- cloud saves (for many games, at least)
but makes you dependent on the Steam network (which isn't reliably available for everyone - if you've had good experiences so far then you should be alright) and their client (some people find it awkward and frustrating, others like it)