Hi MattOKC and Welcome
You ask some good questions and I hope other people who know more than I do will share their thoughts, but for what it's worth here is some of mine ....
It sounds like you are considering how the term fraud would apply to different areas such as identity , knowledge , and authorization .
I think there is often a lot of gray areas between people who are outright frauds and the ideal you described.
If a tribe is willing to give out this information, it should be relatively easy to figure out if someone claiming enrollment in a tribe is being truthful, but if people don't specifically say they are enrolled, it seems like it gets a lot murkier.
People often claim to be "Cherokee" or some other tribal identity, when what they mean is that they believe they descend from someone who was a member of one of these tribes , and for some reason , which may or may not be valid, they believe it's OK to claim this as their own identity.
This can be a gray area because there is differing opinions as to the amount of emphasis unenrolled people should put on one part of their ancestry . There is sometimes legitimate tribal leaders and Elders who, under some circumstances, would support these descendents in their claim to a Native identity .
Then there is the problem that a lot of perfectly nice people were told by someone in their family there was some Native ancestry back there and they repeat this without it even occuring to them that maybe they should be skeptical about the story about Princess Cornblossom.... Most of these people don't try to exploit this aspect of their identity , so even though they may be mistaken, or a bit warped in how much emphasis they put on this, unless there is also exploitation , a sense of entitlement , or a stubron avoidence of the truth, I don't think these people are usually frauds.
When it comes to knowledge, even Native people who have a lot of real traditional knowledge can also have unusual personal ideas. A recent example of this is the Camel Eye Treaty which is now listed under frauds, even though some of the people who have been sucked into believing this are enrolled Mohawk people. So I guess it's possible for a belief to be untrue , but the person who believes this to be completely legit.
I'm not sure what you mean when you ask about competant respectful non Native people teaching about some things. It seems if a person was competent and respectful , they would know some things are not rightly taught outside of the context of the entire culture, and they would know they couldn't provide this, so if they were competent that wouldn't try to teach it in the first place.
Probably one clue that a non native person is teaching something they shouldn't be, would be if they were teaching something or performing a ceremony which some Elders say should only be taught or conducted in the original language.
Authorization is also a difficult question because it seems there is often different opinions within a tribe about who should be authorized to do what. A good example is the many Native people who disagree with some of the people Leonard Crow Dog has authorized to lead ceremonies.
On the other side of the spectrum is someone like the author Rupert Ross. He is a lawyer and after numerous experiences with Native people who became involved in the non native legal system , he wrote a book explaining what he had come to understand about the Native world veiw, and what happens when this world veiw has to function in a society where the rules have been created by non native people. The book does seem to be quite accurate and is written from the standpoint of an honest concern for people who's cultural values often puts them in a situation where they are at a disadvantage in the non native justice system. I don't think Rupert Ross is anywhere near being a fraud, and with indigenous peoples being so overwhelmingly outnumbered by non native people , I think non native people do need to have a role in teaching and offering insight into what creates problems for the Native community.
The way this message board is set up there is a catagory for frauds and research needed. The catagory frauds could probably be rightly subdivided into delusional / mentally ill, / exploiters who don't know any better/ , and exploiters who are outright liars who don't care / and people who are dangerously abusive. I guess what they mostly have in common , is in some way, what is being claimed, is seriously disconnected from reality.
Personally I would be more comfortable if there was more objective criteria in the definition of fraud - but many seemingly clear cut definitions can be complicated by other considerations . For example, it's generally agreed on that charging for ceremony is almost always a sign there is a serious problem , but what if the ceremony is part of a package which includes meals or accomadation or some form of genuine psychotherapy ....? What then ...? and here is where the problems in making a definition come in...
What I am saying here is just my own understanding of this , and much of what I think has been formed from participating here . Hopefully some other people will offer their own perspective or be able to answer your other questions -.