Pvt guitar lesson rules?

The general rule is: private teacher sets their own rules.  They could charge you for not showing up, charge you double, or make you pay with Skittles. It’s their business.

Yes, that's absolutely fair and is typical.  If you had canceled the lesson you were going to miss, then they could have filled that slot with someone else; you wouldn't have had to pay but they still could have earned their money for that time.  What's not fair is for them to lose out on their expected income because you were irresponsible and overslept.

When you arranged for the lesson it meant that the teacher couldn't book anything else in that time slot. You oversleeping and missing the lesson doesn't change the fact that the person dedicated that time to teaching you, and you not showing up means that time was already reserved. Act like an adult and pay up. And in the future you ought to try and be more responsible. 

Most definitely it is fair. You are the one asking for the lessons, he didn't come to you offering. You are paying for his time, whether or not you show up is up to you. He has every right to charge you, no matter if you are there or not.

Yes, absolutely.  The teacher set aside that time to teach you so you owe them for their time.  Same is true if you miss a doctor's appointment.  

Most private instructors will discuss their payment and cancellation policies. If you have not had this conversation, now is the time to do it. 

Yes, it's fair. You and your guitar teacher have a verbal contract: payment in exchange for lessons at a specific time. Your guitar teacher set aside the time. You didn't show up. You still owe payment. That's fair.

If you had called and given the person notice, then some alternate arrangement could have been made.

Of course it's fair. He could have been teaching someone else so he lost money. That's how the adult world works. You still have much to learn it seems.