If the CG of an airplane moves forward, would it fly a faster or
slower airspeed in a descent?
Hang gliders and "trikes" (powered hang gliders with seats and wheels) use CG-shift as the sole means of pitch (and roll) control. Anyone who has flown such aircraft will tell you that the answer to your question is "faster".
However, I remembered that a forward CG usually decreases performance
(and thus speed?) due to a larger tail down force needed to counteract
the forward CG, more wing loading and more drag
If the airplane is re-trimmed to continue to fly at some given airspeed at the original power setting after the forward CG shift, drag will generally be increased due to the increased tail downforce. So the climb rate will be decreased, or the sink rate will be increased, depending on the power setting. Similarly, if the airplane is re-trimmed to continue to fly horizontally at some given power setting after the forward CG shift (or to maintain some given climb rate or sink rate), the airspeed will generally be decreased due to the increased drag associated with the increased tail downforce.
But if you leave the elevator trim fixed as you move the CG forward, the tail isn't going to magically create more down force so as to decrease the airspeed. Rather, you'll end up flying at a lower angle-of-attack, and so you'll see an increase in airspeed.1 If you are flying on "front side of the drag curve", as is most often the case, this will cause an increase in sink rate (or a decrease in climb rate). If you are flying on the "back side of the drag curve", as is the case in "slow flight", this will cause a decrease in sink rate (or an increase in climb rate).
I also don't know if a power off descent vs level flight changes the
fact that a more forward CG, increases drag and decreases airspeed.
There's no fundamental difference in this regard between a power-off descent and level flight. It's just a matter of what are you holding constant as you change the C.G. position-- elevator trim position, or altitude, or airspeed? See above for more.
- A careful analysis of this situation shows that the tail downforce has in fact been increased. But the result is not a decrease in airspeed.