What defines a healthy relationship between a man and a woman? Is arguing and anger a part of a healthy range of emotions?

Yes no maybe arg. If one wants something to work that is much invested in, it can be frustrating when it is not working well. Anger is a feeling that notifies us that we are being hurt, threatened, or our boundaries are being eroded. Now it is what one does with the anger at this point. If it energizes and emphasizes in a manner that is effective, that is good. Sometimes it punctuates and gets the others attention.
NO. Arguing and anger is not healthy; you should see a counselor to learn healthy communication skills and work out the differences you have.
Depends. Conflict is inevitable and essential. It can be destructive, but if handled well, it can defuse situations that might cause bigger problems later on. Studies have found that the more unexpressed irritants partners have, the less satisfied they tend to be. This does not mean that every nuisance should be aired. IIt does mean, however, that it is important to recognize real problems and address them.