Hi,

" I am trying to find a way where you can search something from someone's profile (such as uploaded files), without searching any of the profile itself"
Yes you can by turning off the profile search provider and turning on the file search providers that are available in the web.config

"I know that you can get rid of the profile search, but could google still search it, and is there a way to set permissions, such as for profiles, in MonoX?"
Yes it can search it, search providers are not related to publicly accessible pages in the MonoX, so if you want to "hide" profile pages from Google you can use robots.txt file to tell the Google Bot not to crawl the profiles, if you want to remove them completely then you can use MonoX page permissions in order to limit the access to profile pages (MonoX portal administration -> Pages -> Right click -> Page properties -> View or Edit permissions section).

Regards