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It's an interesting question which can get you quickly into deep physics. The simple way to view it is the light being made up of photons, which can be viewed and act as particles. Then, when the photon interacts with another particle, phenomena occurs which make them look like oscillating - so from the wave domain - like interference for example. But this ...

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Electric and magnetic fields can and do exist in a vacuum. Electromagnetic waves are just fluctuations in electric and magnetic fields. In a vacuum (meaning no charges or currents, which do require the presence of matter), then the solutions to Maxwell's equations are electromagnetic waves.

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Young supernova remnant release a substantial amount of radiation as they expand into the interstellar medium. In the free expansion phase, the outgoing shock wave heats up matter to $\sim10^6$ Kelvin, producing thermal x-ray emission. Throughout their lives, the remnants are responsible for quite a lot of non-thermal emission, including synchrotron ...

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I assume you are talking about neutron stars. Some supernovae leave nothing except a black hole, and these dense remnant objects are typically surrounded by a lot of more scattered material that was blown off before and during the supernova. Neutron stars and nebulae emit a wide range of EM radiation by a number of mechanisms: straightforward thermal ...

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