Nope, any changes to Espionage level are permanent and do not require your spies to be continually assigned.  You only need them there in order to increase the espionage level.

I'm pretty sure that you need a placed spy if you hope to steal tech from another civ. But maybe that changed so you only need at least one on civ-wide duty. Been a while since I played lots.

  Sometimes they steal one nearly every turn,  sometimes never during a game [DA, Metaverse games].

  I've thought it depends on what type of buildings they are on,  how many are placed,  how long they have been there,  which planet they are on?  However I haven't noticed any strong correlation;  I use spies for sabotaging buildings on bonus tiles (factories,  research labs) and stuff like galactic achievments (Restaurant of Eternity was a recent one);  or sabotaging all a race's labs when they are researching Tech Victory.

A few games ago, I left 4 spies on the Iconians for a long time after reaching the advanced knowledge level.  A long time.  A long long time.  And I did get one tech stolen.  One.  The next game I used a custom race with the Krynn tech tree, which allows improvements to be built that increase the espionage skill by over 50%.  I did the same thing, leaving 4 spies on the Iconians through most of the game, right up until their last planet was taken.  No techs stolen, even with the espionage skill boosted by the Krynn buildings.  So I gave up, I'm not going to do that ever again.  It might happen once in a blue moon, but it's not worth it.  This was on ToA, YMMV if you're on DL or DA. 

That's a random event, though - it has nothing to do with actual espionage.

Or, if you're playing with a mod that lets them colonize, just leave their worst planet alone - no need to give them one of yours.

I actually can't take advantage of this event on TOA, as I have the "no tech brokering" option on all the time, and the game counts the techs the minor stole as qualifying for that. It's still pretty significant, though, as it can cause the minor to become quite powerful if the race they stole from was advanced enough. A game on TOA without my minor colonization mod had the Akilians steal so many techs that they developed the fifth-largest military in the galaxy and played a key role in destroying the Dread Lords that invaded in the late game.