If I change z-index of #header1 to 1, the second level of my drop down menu disappears behind the #main-content that has z-index: 100.
So, what should be the z-index of #main-content, #header1, .cse-overlay, and #nav?
I have one question regarding implementation of the solution provided: I have checked my Google custom search engine account for default+en.css file that also needs editing. I found default.css file that neither feature .gsc-modal-background-image class nor .gsc-results-wrapper-overlay class. My CSE’s default.css file does not even feature z-index.
From where I can download default+en.css file for my CSE.
You really should not make changes to any of the WordPress (or Google) style sheets. Changes should be in the form of overrides to the WP styles and should be made on your local.css stylesheet (which you don’t seem to have). The reason is because any WordPress update to the master WP styles would wipe out your changes. So it is best if you make your changes on local.css… and be sure that it’s loaded last so it overrides the WP style sheets.