Dreamweaver has no issue with using CSS. Older versions used now deprecated or obsolete html attributes (like BGCOLOR) to style things, but CSS was available and the program understood most of it (especially basic things like color, background-image,etc). Adobe moved away from using the old html attributes for style in CS6 back in 2012. Current versions default to css property/value sets, though there are still some units and now-standard properties the program has issues with.
If the site uses .DWT Template files, all you should need to do is create an external .css file, then in the .DWT, link to that .css in the <head>. That edit should then propagate to all of the child pages made from the .DWT. After that it's a matter of removing html attributes from the .DWT, propagating the changes, and adding equivalent css to the external .css file (no waiting for the child pages to update there since only the external css is being modified).
Which code editor have you been using up until now? I ask because DW is merely a glorified code editor + FTP and site management tools built in. So there's no secret sauce required. You use DW pretty much as you would any other code editor.
"<BODY BGCOLOR=#000000 TEXT=#FFFFCC LINK=#00FF33 VLINK=#0033FF ALINK=#FF0000>"
The bigger issue here is that your friend's site is grossly outdated. We haven't used HTML code like this in a very, very long time.
And then there's the prospect of maintaining an 800+ page static HTML site. Ugh! Stop the madness. This has to be rebuilt responsively and with a dynamic (database) solution if possible. An online CMS like WordPress might be the better option here. Wordpress.org is open source and most reputable hosting plans support it.