1. Active spies only disable an improvement; they cannot destroy it.
2. That's pretty much it. If you don't want your active spies to be nullified, don't ever drop any less than five on a given civ. Ten is even better. You'll still lose one or two, but they can't keep up.
3. Passive (civ-level) spies cannot tech steal. Active (planet-level) spies cannot increase your espionage level. (Don't ask me, that's just how it's working.) The benefits of achieving advanced via passive is that you don't wind up losing scores of spies in the process, as opposed to the old all-planetary system.
4. You're still going to be sabotaging things, but generally you'll want to pick things the AI doesn't care about-which can change from game to game, but if you can find a stock market that's normally a safe bet. One other hint is to spy on an improvement that's in the process of being built (particularly if it's a counter espionage center), as the AI generally will not check back on such improvements and simply leaves spies there alone.
5. It's either high or advanced-I think it's advanced.
6. Essentially, yes. It will be a pseudo-random tech from the opponent's tech tree. It would seem that this follows the same general mechanics as tech stealing from invasion, in that late game you're much less likely to steal techs, presumably because you already have the vast majority of them and it keeps rolling one you already have, but this has neither been proven nor refuted, to my knowledge. The chance of tech stealing is low enough that you can assume when it happens you'll get something you didn't already have-whether it's useful is another question entirely.
I have no idea what you mean by "present on the planet"; planets don't research individually.
You can't choose what tech to steal, nor what type, level, etc.
7. Korath and Drengin don't get counter espionage centers in their trees. The AI as a whole doesn't prioritize yellow techs, other than the Terrans, so they won't have them very early. The Krynn start with the tech due to their SA. As far as spies actually battling it out, I haven't noticed that much of a difference-the primary factor is economy. Krynn and Iconian will pretty much kick your ass there, though, so concentrate on the others.
8. He is informed of its presence on the next turn. If he looks at the planet in question, he can find it on the turn you place it, before it does any "damage" (apart from morale/farm structures, at least), but to my knowledge this is not something the AI does-while I don't recall ever having a spy nullified on turn 0 of its placement, I've nullified more than a few AI spies on said turn.
-Firstly, you would have brought the Drengin economy to its knees (dependent on how many other planets he has, certainly, but if he doesn't want to lose homeworld pop [<20% approval] he'd have to lower his taxes somewhat, which means less money from all his other planets), both by forcing him to have his taxes lower and secondly by having him spend 25% of his income on fighting off your spies.
I have yet to see any indication that a planet's morale significantly increases a planet's tendency to revolt, although it may do so marginally. If it did so, the AI would choose a new capital in relatively short order-sometimes it forgets, but the empire is still alive, just without a "capital".
I've seen stories of planets branching off of a race in TA, but I've yet to see it based on my own playstyle-basically a duplicate of the original race with a different name and perhaps different ethics/etc. If the planet had simply revolted due to a combination of neighboring influence and low morale, it would (probably) be the strongest neighboring influence (>4x as much as native). To my knowledge, other than the instance where one race becomes two, there's nowhere to revolt to if there isn't a stronger neighboring influence.
I'm not sure if the split counts them as a major or a minor, though, particularly as I've never seen it.
