When enabling and using the "remember me" cookie option in the php_include plugin, will it also allow protection of media files (beyond just php) if the protection mechanism being used is new_rewrite? I noticed there is not any configuration options with the new_rewrite protection plugin, but I'm guessing it is probably working in conjuction w/php_include. I could be wrong though. new_rewrite protects media files, unlike php_include (which only protects php/html files), but there is no way to configure the "remember me" cookie settings for new_rewrite unless it also works from php_include.
Yes, it can protect any type of files. You configure php_include plugin as you wish, and it will affect new_rewrte as well.