For X-rays, the amount of radiation (if any) will be proportional to brightness. The energy (determined by the CRT high voltage, called kVP in the medical imaging field) is not affected. This is one reason many monitors and TVs are designed with brightness limiting circuits.
In any case, there will be virtually no X-ray emissions from the front of the CRT as the glass is greater than an inch thick and probably contains some lead for added shielding. Also see the section: Should I be worried about X-ray exposure while servicing a TV or monitor?.
Electromagnetic radiation (EM) is produced mostly from the deflection yoke and to a lesser extent from some of the other magnetic components like transformers and inductors. Depending on monitor design (some are specifically designed to reduce this), EM emissions can vary quite a bit. Frequencies range from the 50/60 Hz of the power line or vertical scan rate to several hundred kHz in the AM broadcast band. The intensity and spectral distribution will vary depending on horizontal and vertical scan rate.
A totally black screen will reduce X-ray emission to zero. It will not affect EM emissions significantly as most of this comes from the magnetic parts, particularly the deflection yoke.
There is no measurable microwave, IR, or UV radiation.
I refuse to get into the discussion of what, if any, health problems result from low level EM emissions. There is simply not enough data.