A bit on conditional logic:

If we have an affirmation A--> B

then the inverse is what you call the incorrect negation !A --> !B

converse is what you call the incorrect reversal B --> A.

Yes, these two are contrapositives of one another; no, they are not inverses of one another.

The answer to the rest of your question is essentially yes, with one caveat: if you're diagramming parallel flaw questions, you need to know which is which.