some sites provide modified index files as well. just like you did with the .css file, rename the old index.php to indexOLD.php and upload the new one the main wordpress folder.
it looks like (from the instructions at least) you can just upload the whole thing and dump it in your main directory. it could be that your css is just being annoying for you, so try editting the css file so the images point to full paths (https://yoursite.com/image.ext vs. image.ext)
Root: it’d prolly be a good idea to include a section for #rmenu styling in the trident CSS. just a copy of the menu stuff would be enough to get a new person started.
if all of your wp files are in that one folder (formerly blog, now news) then i think its just a matter of changing “WordPress address” in your options page.