Spies do not destroy improvements, rather they disable whatever benefits they generate so long as the spy is present. Aside from that though they can only be used to cancel out spies planted on your own buildings.

You can kill population by planting a spy on a farm, or slow their research by planting one on a lab or research capital, etc.

Yes, yes and yes.
As kyro stated, you can kill off a massive amount of a planets' population by spying on a farm..however the number of victims is only as much of the population that is tied to that farm. In other words, if the base population of a normal planet is 6 billion and theres one regular farm on it that increases the population by 3 billion..you can only kill off those 3 billion. That is of course if your spy isnt nullified by that race for more than a couple turns.
Any other improvement you place a spy on, is in effect 'turning it off'. Meaning that if its the manufacturing capital, then that 25% bonus does not apply for as long as your spy is there. Side note; the only things that can not be spied upon(as far as ive seen) are the trade goods, galactic achievements aand the minor races for some odd reason? Also, a big thing that cannot be shut down is the Spaceport..which i personally think is a mistake. Its just as vital as a farm or factory, if not more so, and you dont have any effect on it?

As for the last question, I think ive noticed that if you place enough spies in a races' territory(say upwards of 5) and theyre able to stay there for a few turns..that race will get pissed off enough and declare war on one of its neighbors. I may be wrong about this(someone correct me if i am). Ive done it a few times and noticed that a new declaration of war has broken out between two races, one of them being the one i was spying heavily on. I think youd have to be careful as to not be the one that is being challenged, but i think if youre on semi-good terms with that race they wont suspect you. But rather theyll go after either their closest neighbor or the one that they like the least. Since no one can be 100% sure who is spying on them, unless its a really hostile relationship to begin with. It makes sense, because that is exactly what i would do. Im not sure if it works better on certain races or if others are wise to the action, but its def an improvement on behind the scenes diplomacy.

why pre-emptive spy? just research and selectively build the counter-espionage center. it was added in the last beta and unless you dont have that yet, i highly reccommend it. its not a particularly hard tech to research and while it takes up valuable realestate, it effectively blocks any attempt to be spied on and sabotaged. ill usually only build it on my most important planets, i.e. the ones that are most likely to be targeted for spying. Economic, manufacturing, research planets..anything with a resource on it and any with high populations and farms(so i dont fall victim to my own evil 'exploitive' tactic.

though id like to add that i dont go around killing off billions of innocents for no reason with spying on farms. i use it as a war tactic, hit a 20B planet a couple of weeks before my transports get there and BAM, take that planet now with only 12B and 1-2 transports. though i understand how some might argue that starvation is worse than a laser blast to the brains.

Spies on planets also pick up information on players. Eventually technologies and other data get stolen by those spies. It's a two-fer.

It's a two-fer.

For folks who are still pining for old-school DL intel, this is a two-fer at the expense of comparatively no-brainer opposition research.

I really like the DA added option to disable an enemy planetary improvement, but I'm having a hard time getting over my resentment about "giving up" the passive intelligence gathering.

Differences from GC II
1) Spies can disable foreign improvements or disable foreign agents on your worlds
2) GC II standard espionage cannot be pursued but as a side effect of disabling foreign improvements you get standard espionage data like it was in GC II
3) If you build an agent you can look at any improvement of any planet you are aware of (just keep going and not place it). Quite a good collateral effect...

It would be nice to add back the silent collection work that was in GC II by placing agents on planets without hampering improvements. The more agents the more I know...
I'd like to know what my friends are doing... just in case...

I really like Robert's idea of spying on the Entertainment Centers.

One question;

Can't we just have an option to disable spying altogether and be done with all this trouble!

Repost from beta reports section

Tweaking the spy system
By Scintor
Posted January 9, 2007 12:37:04
After reading through the posts here and playing through a Gigantic-Abundant game, I have some Ideas that could tweak the espionage system so that it would be more usefull and scalable to all galaxy sizes.

The first problem I noticed was that spies could only be used in an aggressive way. Now, I tend to play toward an influence strategy, and seldom get into wars. I really have no real interest in trying to cripple my neighbors. I am very interested in getting good intellegence on all my neighbors including minor races.

My suggestion is to have a place to put 'sleeper agents' for each race. These sleeper agents would not cripple any improvements, but would do the secondary tasks that agents do like getting intellegence on the civilization and having a chance to steal techs. The compensation for not taking out any improvements would be that they could not be nullified by other agents. This would allow you to gather intelligence without starting a covert war.

The second suggestion is a change to how counter-espionage centers work. Right now they seem to be a really bad investment in rescources unless you are working on a really small map only a handful of worlds. On gigantic maps where I have 200+ worlds building agents is so much more cost effective as to make them useless.

The only change I would make would be to make is to allow building a counter-espionage center to remove (not nullify) an agent from your world. The agent would be sent back to his home civs agent pool, not killed. This distinction becomes increadibly essential on Gigantic maps when you get the 'Every world gets a spy' event. On smaller maps, you have around 20 agents to deal with, which is a difficulty, but can be dealt with in time. In my latest game, I got the event and got 236 agents in my empire! This is an impossible number to ever negate. If I were able to remove them with counter-espionage centers, I could eventually remove them all. It would be a long tedious process, but possible. On the other hand, I do not see it as reasonable to have to build these structures on all my worlds simply to protect myself from a random event.

This leads me to the Super Spy Super Ability. All the discussions I have seen on the board seem to universally pick this as one of the worst and most useless super abilities. I would make two changes that I think would make this ability on par with other Super Abilities.

First I would give all their worlds immunity to agents being placed on them, as if they had buiult a counter-espionage center, without the morale bonus. This would make the only way to spy on them is 'sleeper agents' as outlined above.

Second, I would make their agents unkillable. Any time one of their agents was nullified, instead of being killed, it would be removed and sent back to their agent pool.

I think that this would make a Super Spy race one that could really use the espionage system as a path to galactic conquest.

These are my ideas that I think would make the espionage system much more flexable and scalable and make the Super Spy super ability one that people would rreally use.

Scincerely,
Scintor