Sorry I was premature in closing this. I’m still unable to get the first issue working – adjust the menu item height independent of the site header. Right now, changing the menu height also changes the site header.
I added the CSS indicated in but changing the menu item height still affects both the menu height and the site header.
Sorry for the confusion. It’s working. I got thrown by expecting Customizer to show me the change on the fly. It didn’t. But once I published the change and viewed the site again, it came up correctly. Thank you for your patience.