Is there a key combo or way to set one for copying a single line, like there is for deleting a single line using Ctrl+E?
Open Advanced - Settings or Configuration - Editor - Miscellaneous and check the configuration setting Enable copy/cut of current line with no selection active. The current line with the caret (text cursor) can be copied with Ctrl+C to the active clipboard and with Ctrl+X cut to the active clipboard after closing the Configuration dialog window.