Impossible to vary square wave FREQUENCY output based on a PWM input?

Everyone is a moron. Don't listen to him.

Well, there you go.

So one solution would be to transform your incoming PWM signal into a DC signal that varies with the duty cycle of the PWM signal. A simple R/C filter may already get you in that direction - in fact, it may be the solution in itself. Give it a try?

Me too. You could use it to measure the duty cycle of the incoming PWM, provided that the incoming signal is of sufficiently low frequency and your demands on measurement resolution aren't too high. And you could use a timer to generate a PWM signal of adjustable frequency as well. Good thinking!

Yes, it's quite well documented in the datasheet of common microcontrollers. For instance, if you were to us a classic Arduino Nano or UNO, you'd be looking at the Atmega328P datasheet, which has a few chapters dedicated to the use of Timers, including PWM signal generation.
In addition, if you google 'Arduino pwm timer' I think you'll find something. Part of that 'something' is probably also sets of ready-made libraries that you could use.

So my question to you is, really: given your sound reasoning and good ideas so far, what's holding you back!?