At what frequency does the wavelength = the height of the wave amplitude ?
At 7.7646 x 1020 Hz. The associated wavelength and amplitude is 3.861 x 10−13 m. The electron Compton wavelength is 2.426 × 10−12 m, which is 2π times this amplitude.
The wave height = the physical space the waveheight occupy in space, similar to the wavelength. My assumption is that the wave height of the basic electromagnetic wave is fixed.
Correct. Take a look at some pictures of the electromagnetic spectrum, note that the amplitude is the same regardless of frequency, and note that the dimensionality of action h can be expressed as momentum x distance. Also note that the reduced Planck's constant ħ is h divided by 2π.
It's important to note that an electromagnetic wave is an electromagnetic wave. Some people will tell you it's an electric wave and a magnetic wave which generate one another, and therefore no medium is required. That's not true. Check out the Wikipedia electromagnetic wave article and note this:
"Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field".
What people call the electric wave is actually the spatial derivative of the electromagnetic wave, while the magnetic wave is actually the time derivative. They are merely two aspects of the same wave, not two different waves. And as Maxwell said, "light consists of transverse undulations in the same medium that is the cause of electric and magnetic phenomena". When an ocean wave travels through the sea, the sea waves. When a seismic wave travels through the ground, the ground waves. When a gravitational wave travels through space, space waves. See LIGO:
"Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity. Einstein's mathematics showed that massive accelerating objects (such as neutron stars or black holes orbiting each other) would disrupt space-time in such a way that 'waves' of distorted space would radiate from the source (like the movement of waves away from a stone thrown into a pond)".
The same is true for an electromagnetic wave. When an electromagnetic wave travels through space, space waves.