Can I use a Xoops website commercially and make money from it?

Yes, there are no restrictions on what kind of services, you can offer with your XOOPS website or how you charge for them.

Some other considerations :

Legal (Have to do)
-----
>You may use Xoops for anything you want.
>You must leave the credits in the source code.
>You do not have to have "powered by" or any kind of display credit
>You may redistribute, even sell the code.
>You may not restrict the redistribution rights of the code
>You may change, add to, delete from, and intergrate with the code.
>You do not have to release your modifications.
>If you do release your modifications (including modules) they must be GPL or less restrictive.

Polite (Would be nice)
------
>Give Xoops and the hard working developers the credit and recongition it deserves
>Release your improvements
>If you benifit from Xoops - GIVE BACK! Money, Time, Code, or Something Else.

see also this FAQ HERE

and Here

This Q&A was found on XOOPS Web Application System : https://xoops.org/modules/smartfaq/faq.php?faqid=164