Please give your opinion as to what payment should be per half hour vs. per hour.
Depends on where you live and how good your teacher is. When I started piano lessons, it cost my parents $18.00 per half hour. Now, it's $19.00 per half hour. It all depends on:
1) Area
2) Teacher
3) Length of lesson
4) Level
However, I have a friend who takes piano lessons at someone's house and she can come to classes anytime as much as she wants, as long as she wants for $30.00 a week.