Changes from "customize" not happening

Hi,
I'm trying to customize the site. When I change font/link/whatever color and save, it doesn't do anything. Just reverts to default.

I created/activated a child theme and tried putting some stuff in the style.css, but that also didn't do anything.

Other than changing link colors, my biggest issue is the weird white header with the shadow. I can't seem to change the color of the header (h2) and get rid of that shadow. Go here to see what I mean:

http://www.transcriptionstudio.com

Also, one other thing, how do I change font colors?

Note: I tried disabling all of my plugins but still having the same issue.

Thanks.