You're a real guru, aren't you?
Well your applet-box command above did wonders. I selected a 6px value (left and right) and this time, the white icons complied. It does now indeed looks much better.
I am using (I should have said it before), the "regular" Cinnamon theme.
I previously downloaded and installed the latest cinnamon.css but it did not change anything, even the Me... Menu bug was still there.
Thank you very much. This is solved.