You do not need any sort of educational accomplishments to teach at the university level. I have had several professors who did not have a bachelors degree and have heard of professors who never even graduated from high school. That being said, those professors were all special cases. They were former ambassadors and CEOs etc. who where qualified to lecture on their areas of expertise while raising the prestige of the university. Unless you have some sort of special experience that will instantly make the deans overlook your lack of a graduate degree you will likely find it impossible to get a job teaching as a professor. Some of the local community colleges may hire you, but that is about as far as you can go. I suggest (unless you have held some sort of prestigous position) you get a job as a TA.

Yes — and may even need your doctorate or a very impressive performance portfolio. Take a look at the music departments of some colleges and see what credentials the professors list. Most colleges make a big point of advertising the percentage of their professors that have seminal (final-ultimate) degrees to attract students to their departments.

Yes, many colleges require a masters or doctorate degree for their professors.

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