1) I edited the parent theme CSS and the changes took.
2) I moved those edits to the child theme, activated it, set the parent theme back to default (i.e. before my changes), and the changes went away.
3) I added some new CSS (classes and other stuff) and those changes worked well, but the CSS changes that also exist in the parent CSS (base.css) don't work.
Why? How to correct this?