The variable $cat and $single can be used for checking whether you are in a permalink page, category page or the main page. You can create a conditional statement and include the desired stylesheet that way.
Make the permalink path in the /skylog/year/month/day/post-name format. The code is there on Options>Permalink page. WP for some reason does not parse the calendar and archive links if the permalink is not in the above format. Bug?!
If you are using Apache, .htaccess should work but it won’t work on IIS and other. First confirm from your host whether you are using Apache or not.
If you are using Apache, and .htaccess still does not work, you might want to use the AccessFileName Directive to force Apache to look into .htaccess. More info is here: https://httpd.apache.org/docs/mod/core.html#accessfilename .