Independent Publishing as a University Affiliate What are some things to keep in mind while publishing as a university affiliate? By this I mean positions that allow credentials like for being a third party instructor, counseling etc. Is it ethical to use university credentials in those cases?

Also what kind of a difference does funding make in this case, provided the affiliation does not include any terms on intellectual property? This is assuming it is not completely unethical to use credentials that were provided for a specific purpose, even if not explicitly.
First, you don't need university affiliation to publish papers. Different universities might feel differently about your situation, so you should ask someone, perhaps in the department for which you teach. They might not want you to use the university's name if you aren't on the payroll, especially if you aren't subject to their normal rules. 

The one important thing that the university might be able to do for you is provide IRB advice if your research involves human subjects in any way. 

Other than that, you can probably use anything that is merely descriptive, such as "adjunct instructor at H*d University". 

But, "Independent Researcher" may be your best "affiliation". The reviewers will be interested what you write in your papers, not your university. Your email address will indicate some association in any case.