When changing tire size (for example: from a 235/45-17 to 225/45-17) you can change either wider or narrower as long as the overall diameter does not change more than 3% (so that I will not screw up speedo and other monitoring devices)?

In the above example the diameter for the 235/45-17 is 25.4 and the diameter for the 225/45-17 is 24.9 so...

25.4 - 24.9 = .5
.5 / 25.4 = .019685 or 1.9685%

Getting back to the question, is the key 3% or is it some other percentage?

3% isn't fixed by any means.
Really, the goal in increasing or decreasing the width of the tire is to maintain the same overall diameter. There are some margins allowed in increasing, or decreasing the overall diameter, but the percentage isn't necessarily fixed at 3%.

It depends on a number of factors, but most important is what you the driver is willing to deal with. Increasing the diameter causes a couple of issues, rubbing, mis calibrated speedometer, and slower acceleration.

The amount your car is lowered will most likely determine the rubbing factor. Stock heights certainly allow for more room.
There are calculators on the net that can show what your corrected speedometer will read. What you're willing to accept is up to you.
And slower acceleration will definitely be noticeable. Just chip the car, and that'll go away. :)

Good luck