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.