Spies - Do you need to leave them there?

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.

Plus if the race you're spying on surrenders or is otherwise wiped out, you lose the spies you had assigned to them.  So reassign them wisely. 

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.

Do they EVER steal techs?

I'm mostly playing campaign so far but I have NEVER seen a spy steal a technology no matter how many of them I throw at an empire.  (I really had hoped for some juicy Dread Lord ones, too...)

  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.

I'm fairly certain that spies can't steal from minor races, which is what the Dread Lords technically are.

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. 

Funny thing is, in my last game (on immense map), a minor race stole like all techs from the biggest race in the galaxy (no not me at the time:p), a little bit odd!

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

When a minor has that event and the race they stole from was powerful, I instantly change strategy to get the techs from that minor.

The simplest way, I've found, is to threaten them into gifting them to you.  That is, get an invasion fleet overhead, declare war, then offer peace for that price. 

One trick is to gift them a planet of yours deep in your space (after you clear it of all but one population, of course).  Then, even if some other race invades them, they remain in the game.  Meanwhile, you can invade their home planet, they still exist as a race, and then offer peace for the price leaving them with only the cheap planet you gave them.

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.