Obviously Charles is using Telepathy to do all these things and I am not sure there is anything canonical on how he actually does it, ie via brain waves.
In SUPERPOWER wiki it states,
Telepathic Communication, which is the ability to transmit information
from mind to another, and Telepathic Perception, which is the ability
to receive information from another mind.
And has this useful piece of information
Does not work on mindless beings (corpses, animated objects, robots,
When sending or receiving information through the air the use of radio waves (electromagnetic radiation) is at present the most popular method of doing so. So, because telepathy does not work on dead and in animated objects, this shows that brain function is needed and sending and receiving information directly to the brain requires some sort of electromagnetic radiation in wave form to be emitted from the brain. What you want to call that could possible be considered "brain waves" I guess.