Yes you can do just that.  You can send spies to sabotage entertainment/morale buildings, industries, research labs or whatever.  You can steal techs as well.  But what you cannot do is manipulate players into doing things directly as far as I know.

If you find a miserable planet and infiltrate their entertainment buildings, you can quite effectively cause revolutions.

You can brive some players into attacking orther players. Certain races are better at this than others. When you are the target of such, you are at least sometimes told that the attack was at the bequest of another power but not which one.

My last game I gave or sold ships and technology to the weaker side in several conflicts.

The closest that I can think of for assinating leaders would be to cause a nation so many problems that they dispose the curent leader. I have only seen this happen twice and only remember that the civiliztion was doing poorly and had some plannets that were unhappy. Maybe you can do something similar.

Because the AI's seem to horde Spies alot. And if they don't use them to eradicate yours then sometimes they'll bombard you with them on occasion. The increased economy at higher difficulty levels makes that possible.