How can Electromagnetic Radiation travel without a medium?

If Electromagnetic Radiation can travel through the vacuum of space then it can travel without a medium, but shouldn’t this be imposable? Or is it true that Electromagnetic Radiation uses the medium of existing magnetic fields, such as earths, distorting these fields much like sound waves do to air? And if so how can this [...]

Hypothetically, could something travel faster than the speed of light if it’s traveling in a different medium?

My Optics lecturer said something about how since light travels in a vacuum, you could, potentially, have something travel faster in a different medium, one other than a vacuum.
True or false?