Is it totally random, or are they scripted events within provinces? Is there a limit to the ambushes you can have in the same province? That is, if it happened once, can I be sure that it won't happen again in the same province?

I guess this counts also for 'approach adventurers' and similar events.

I can't say with 100% certainty, but I believe the rabble and adventurers events are random. I do know from firsthand experience that, at least in the sandbox mode, they can happen multiple times in the same province. In fact, in one game I had the rabble event occur in consecutive turns.

Again, I can't say this with 100% certainty, but I believe that the frequency of the rabble event is impacted in some way by the proximity of province's controlled by Brigand Outlaws. I've played a few games where my initial province was bordered by multiple Brigand Outlaw provinces and I would swear that in such games I see the rabble event more often. At least until I take control of those provinces.

Ambush, adventurers, traveling trader,quiet pool and some more - these all are hidden sites (destroyed upon exit), not events.

There is limit only on max amount of sites (10-15). You can meet more than one ambush, I remember 4 once.
From site.var for Ambush:
Terrain:
Plain: 3
Forest: 22
Hill: 7
Swamp: 12

These are weights, not %. Basically, ambush pretty common in forest, rare in swamps and I can't remember one on plains or hills (there are more heavy weighted sites in the pool for these territories). For example, Dragon lair have weight 10, hills only = Dragons in hills more common than ambushes

Thank you for the clarification, Gremlion. I had no idea that was how things worked. Still doesn't take the sting out of stumbling upon ambush sites on consecutive turns in the early going, though. :-)

Actually I usually look upon these encounters as a lot of good as they usually always give something very good unlike most fights. I love getting early first strike weapons for my 2nd or 3rd hero warrior/scout. Or some good spell scrolls for my main wizard. An early Fireball/Lightning is so sweet.

If I cannot take them out then I do the into the past thing and wait to explore that province until I can. which is usually just the same turn or the next.

Thanks all for the information.. yes I love ambushes too, but it can prevent getting the strategist reward if a lone hero is caught. Also I saw that in the first ring around the stronghold (yours or enemy's) ambushes are very easy, in far provinces they get tough. Now that I know that they're more frequent in forests and less in plains, I'll use my lone wizard to explore plains only.

I don't like to go into the past, which I understand is my own limitation. I never back down from an ambush (which, again, I have no one to blame but myself) because it's true that they can bring some great rewards. I just get a little peeved when I get an obviously overpowered one (which happens occasionally) or get them on consecutive turns (which has happened to me a couple of times).

Personally I love the ambushes. They give consistenly great rewards - almost always something useful, even pretty lategame. But I agree they can be nasty early on, and bad if you go for Strategist or refuse to use "Go into the past" on principle, but both those cases equals difficulty +2 right there, so little wonder :)