Your rewrite rule says "redirect /anything to /mediawiki" -- that includes /mediawiki, hence the loop. Unless you add the [L] (last rule) flag, the targets of rewrite rules are themselves evaluated.

I've got php running as Apache->FastCGI->PHP-FPM and it seems to work fine except for some reason I'm getting double REDIRECT directives for some variables. I'm also getting REDIRECT_ prepended onto ...