Do you have any research - even one study - that shows that measurements of brain waves correlate with specific behavior?

I'm not aware of any. Not even one. You can't tell what someone is thinking about or feeling with any specificity from looking not just at brain waves (which are very broad large scale measurements) or even from looking at extraordinarily detailed measurements of activity in various parts of the brain.

You can't even be sure, when the EEG shows REM, if the person is actually dreaming. It generally is the case but there are countless exceptions.

We don't even have any material proof that conscious experience exists.

If you really have any knowledge of this, please sure specific research rather than speculation.