I think that technically, the light from Cherenkov radiation could be used to generate electricity with photovoltaic cells (PVCs). PVCs will generate electricity when an incoming photon has sufficient energy to excite an electron from remaining near the atoms of the cell into the conduction band. For typical silicon-based cells, this requires an energy of ~1.11 eV (eV = electron volts). Visible light covers the range between ~1.6 eV (red light) and 3.3 eV (deep violet), so it can be used to generate electricity with a typical Si PVC (and really Si is a good choice for sunlight PVCs because the absorption range aligns with that of visible light and visible light comprises a large portion of sunlight.) Since Cherenkov radiation is in the visible spectrum (specifically, the higher-energy blue end), it should be possible to use this light to generate electricity. However, I do not expect this to be useful in practice due to difficulty of incorporating the PVCs, financial costs, and so on.

For this answer, we're going to assume that the type of radiation to which you refer is Cherenkov radiation, which is a type of radiation emitted by a charged particle going through a dielectric medium at a speed that is greater than the speed of light in that medium.

(For clarification: "Charged particle" means particle with positive or negative electric charges; dielectric medium means something, such as a container of water, that does not conduct electricity, but takes on an electrically positive and an electrically negative pole when subjected to electric currents.)

The Oxford Dictionary of Physics gives a great analogy for Cherenkov radiation - it's like a sonic boom. A sonic boom is created when something travels in a medium faster than the speed of sound, say a plane traveling in air, and leaves a loud trailing boom. In the case of Cherenkov radiation, the charged particle or particle beam is the thing that travels, the dielectric medium is the "air", and the radiation is the "boom" left behind the traveling thing.

Most of the time, the radiation is very short-lived, so while it can be used to measure certain phenomena, its potential as a power source is very low, not to mention that in order to generate Cherenkov radiation, a large amount of energy needs to be used to send the charged particle or particle beam into a medium at such a high speed. Therefore, using Cherenkov radiation as a power source would be extremely energy-inefficient.

Hope this helps!

From here:
The Cherenkov effect can occur in vacuum. In a slow-wave structure, the phase velocity decreases and the velocity of charged particles can exceed the phase velocity while remaining lower than . ... This type of radiation (VCR) is used to generate high power microwaves.

In theory yes- the first law from the field of thermodynamics says energy cannot be created or destroyed. It can, however, be converted from one form to another. This is what we currently due to generate power, since electric power is not something that really exists in a usable form in nature. Historically, we have taken chemical potential energy (in the form of fossil fuels), burned it to create thermal energy, used that thermal energy to turn a turbine that creates kinetic energy, and used magnets in that turbine convert the kinetic energy into electricity.

Tying back to your question specifically- the light from Cerenkov radiation occurs when a particle in a dielectric moves faster than light in the same medium (note- nothing will travel faster than the speed of light in a vacuum, but when traveling through a non-vacuum, such as a dielectric, light can be slowed down and a particle can travel faster). This phenomena emits light. Given this is a form of energy (particle motion and light), a process could be designed to convert it to a usable form of power for humans. Practically speaking however, I doubt it will be a feasible source of power, as generating and harvesting it would likely use more energy than you get from the process.

Yes, although I would expect that it would be more efficient to use the heat that the Cherenkov radiation would generate to power a steam turbine (since that's normally where we create Cherenkov radiation in the first place, in nuclear power plants).