You can correlate those brain waves with anything really: predisposed to eat oranges to climb hills, likes color blue. Even infinitely small p won't save those studies.
How many constellations can you find on the data points?
Running a linear correlation over them must be a practical joke.
I'm not knowledgeable about statistics and studies like this in general; do you mean this is a "green jelly beans cause acne" [1] situation, where you test for many hypotheses and one of them turns out to be significant?
Exactly, if you test many many things against each other you will always find correlations between them by chance. That's why you always need to start with a "serious" hypothesis.