Are the doomstones and runestones alive, or do they have a soul of a kind or what? The game tell us that they stones needs to rest to get their powers back, almost like the are alive. And also, who built them, and of what purpose?

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Their purpose can only really be guessed at. The one little wrinkle that makes me think away from the whole road marker idea is that the Reman (I think) stones are positioned in the shape of the Apprentice constellation while the Sidri Ashak are in the shape of the Serpent (kinda). People would not build roads and settlements (and road markers thusly) in the shapes of star configurations without it being centered around some point (which they aren't, unless there were more runestones that all orbited White-Gold), and they wouldn't build settlements or forts like that when arable land is at a premium (which it is since they're all pretty much in the Jeralls).

The doom stones I haven't the foggiest. Since their distribution is a little more wide-spread and seemingly arbitrary, I think the road marker idea is a bit more applicable, aside from the stronger magicks that they confer.

Are the stones alive? They have power, that much is apparent, that comes back over time. That is probably what that message is referring to. They can sense a person's heroics and reputation among his fellows. They appear to be pretty well resistant to aging, if they were constructed in the merethic. But are they alive? That is certainly a curious question. My guess is that they are very well enchanted and if that extreme form of magicking lends them a kind of intelligence, then so be it.