How do groundspeed and IAS change during eights on pylons, and how should I manage them?
Answering the easy question first:

No, you should leave the throttle alone once you've begun the maneuver.

As for the other question:

Without seeing your technique, I suspect your IAS is changing because of your climb/descent rate

I don't know how quickly you're climbing and descending, but if you're trying to hit specific speeds at various points during the maneuver, it's likely that you're going to end up flying mechanically and abruptly. An eight-on-pylon should ideally be flown with your eyes mostly scanning outside, and only occasionally coming inside to reference your altitude and speed. 

If you're trying to hit pre-computed numbers rather than looking outside and keeping the pylon on the lateral axis through smooth application of the controls, then my guess is that you'll be climbing and descending more than you need to, and you'll be doing it more abruptly than you need to, which may lead to large changes in IAS.

Have a look at the Airplane Flying Handbook, page 6-17:


  With prompt correction, and a very fine control pressures, 
  it is possible to hold the visual reference line directly on the 
  pylon even in strong winds. .....  It is important to understand that variations in pylon position are according to the apparent movement of the 
  visual reference line. Attempting to correct pivotal altitude 
  by the use of the altimeter is ineffective.


(emphasis mine)

This part of the answer may be entirely incorrect, because I don't know what your flying technique is. If you can give us more information, we can give better answers.