This is still unclear to me, and I assume everybody else has a completely clear picture of it. So I ask.

What defines the prices of GOG games, and where does the money go. Are we supporting/rewarding the authors of an old game when we buy it here, or solely supporting/rewarding those who did the work of making it compatible and available ? What about the modern games, indie or not. What's the difference between buying them here or on their own websites, in terms of who gets what portion of the money ?

And all that stuff. How does it work exactly ? I haven't found infos on that, from the main page.

For instance, suppose I want to (re)buy the "Blackwell" games here. Am I paying the GOG staff, or Wadjet Eyes, and to what proportion ? Suppose I want to buy "Populous". Does it benefit some Bullfrog survivors, or not at all ? Suppose I have pirated a modern-ish game and omg can't live with that, but can't find it anywhere else now that I have the means to pay it. Can GOG help me pay my moral debt, or is it too late forever ?

The money is split between GOG.com and the rights holders. The percentages are not available to us, and are defined by the contract GOG.com has with each right holder. If the developers of Populous still have the rights to it (they don't as I recall), they would get their share.
For newer games, the developers do get a cut, though no idea how much.

The money is split between the current right holders for the game(s) and GOG. GOG's cut is not known to the general public, but it will probably be somewhere in the region of 30%. For older games, by companies that no longer exist, it is unlikely that the original creators will see any money, and only the publisher that still hold the right to the games will get any money. In the case of the Blackwell games, Wadjet Eyes is still alive and active (and the publisher for the series), so they will get their agreed upon cut. In the case of old Bullfrog titles, EA & GOG will share the profit (hopefully EA will then go on and invest some of that money in new and interesting games, while GOG will use the money to make other old games compatible with new computers, and possible funnel some of it towards some of CD Projekt red's game development).

GOG gets a cut of the money. Exactly how much is unclear.

Most of the developers of old games don't get any money. I'm not saying this to discourage you from buying from GOG, but that's the sad reality of it. If, say, GOG were to release X-COM here tomorrow, 2K Games would be the ones profiting from this deal, not Julian Gollop or (the late) Microprose.

With indie games, it's a better slice for them. Since they're independently publishing their games, the developers will be the ones getting the money after taking away GOG's share as middleman.

So, for example, if you pirated Jagged Alliance last time, then you're too late as Sir-Tech, having gone down under, will no longer be getting any money. There are, however, exceptions like the upcoming Carmageddon 1 and 2 releases on GOG, where the rights will go back to Stainless Games, and therefore the developers themselves of the original games will get the money. So, it really varies.

There's no one-size-fits-all answer. For Blackwell, it can be assumed GOG takes a ~30% cut of the sales and the rest goes to Wadjet – that's believed to be more or less the usual split on the market. The same probably goes for self-published games, like Dreamfall.

For older games, it varies a lot. Buying Theme Hospital will presumably be giving a certain percentage to GOG's pockets and the rest to EA, the publisher, and nothing at all to Bullfrog – after all, that's the model the games were originally sold in. In fact, one could successfully argue your moral debt (if any) has always been towards the publisher. It's more complicated in cases like the Sierra back catalogue, now eaten up by Activision who has never had anything at all to do with the games – so here the only one who has any "moral right" to the compensation is GOG, basically, but you could also see it as supporting the franchises and intellectual property, which is very important in the light of recent Kickstarter initiatives, for example.