Note that I challenge this assertion about gravity a bit later on, stating that it itself is a wave, both attracting and repelling at different distances.

Yes, you state that, without proof or support. Electromagnetism and gravity are different forces, both with infinite range but different strengths and behaviors, to the best of our experimental and theoretical knowledge. People measure these things at every scale we can access.

The perturbing electric field in your case isn't moving matter, though; it takes sufficient levels of energy to force an electron to transition to a different energy level, which corresponds (in a very loose sense) with a different orbit. I'll leave that alone, though, because either way, there's an experiment which can confirm or deny my suspicions.

Not all waves have a frequency, either, in the strictest sense; waves can be non-oscillatory. Doing some research into Cherenkov radiation on this matter, as I may be able to formulate a test for this.

Now you're moving goalposts and contradicting your earlier claims.

Also, two electrons with the same rest frame -don't- interact electromagnetically, hence why electrons in cathode ray tubes travel in straight lines.

Yes, two electrons in the same rest frame interact electromagnetically. Of course, if there is not some restoring force opposing their repulsion, they will accelerate away from each other and no longer be in the same rest frame. Cathode rays travel in straight lines because they are subjected to a potential large enough to overcome the repulsion between the electrons. If you have just an electron gun without the rest of the apparatus, the beam will spread out.