Am I allowed to charge money for making a WP site?

yes

Just to clarify….

Yes, you can charge for making a WP site and,

Yes, it is legal to use WP for commercial purposes.

WP seems to be a lot more open and operates a lot more in the true spirit of “Open Source” than other psudo-Open Source projects like Moodle where the developers severely limit your ability to do this by the way they aggressively enforce their trademark.

https://www.alledia.com/blog/general_cms_issues/open_source_projects_not_really_open?/

Steve

If I make a WP modification, basically turn it into a new CMS, do I then need a WordPress link at the bottom of the page?

Read the license: https://codex.www.ads-software.com/GPL

What does it say about modifications and derivative work? What we say here, is irrelevant. Only the license counts.

Good advice from [LostInNetwork]. Your original question was pretty simple and could be clearly answered as “Yes”.

The “basic” answer to your second question is “no”, followed by a “but”…..as in, but there are other considerations when you create a new work from an open source project. That’s covered in detail in the GPL linked above.

Steve

Personally, I wear the “Powered by WordPress” phrase as a badge of honor.