In Vim can you stop the color change of white space characters with 'set cursorline' on?

Question

In this Vim screenshot you can see that when moving the cursor over a line it changes the normal color of the whitespace characters (shown on the left) from grey to black. Can I

Answer 1

Yes you can. From :help listchars (at the end):

The "NonText" highlighting will be used for "eol", "extends" and "precedes". "SpecialKey" for "nbsp", "tab" and "trail".

With this knowledge you can modify your color scheme accordingly or add a call to highlight in your vimrc.