Am I allowed to use xenForo in commercial applications once I buy a license?
Are there any plugins/mods which allow paid file access?
Is there a plugin for Google AdSense? What about other advertisement providers?
You don't need anything extra for Adsense. There are various default ad position templates for ad code, which are not limited to Google ad sense. very easy, you just past the code into the template.
e.g. there are may positions: in the header, above the breadcrumbs, after first post, footer.
I'm not surre what you mean by the other questions e.g. paid file access? - you can have account upgrades, e.g. somebody pays a fee or recurring subscription and they get an automatic upgrade to a different usergroup with more privileges, permissions etc which can mean access to private forums or resource downloads (if you also get the resource manager)
The whole thing is incredibly versatile. if you can't do what you want with the basic xenforo installation, you can be sure there is an addon, either free or paid, that will let you do it.