One of my on-line school's clients is currently a Korean English language training company and I just finished teaching for over five years in China. I think that I could offer you valuable insight into what your potential employer is thinking.
The maximum thirty hours a week should just be to make the municipal government happy since they should only be allowed to hire you for a given number of hours. This would avoid heavy tax fines on their part.
In your contract, your teaching schedule and hours is probably located on a different page, which government types would never set their eyes on. Sounds like your employer is saying that you would be working for forty-five hours a week.
As far as the teaching hour equating to forty-five minutes, you need to clarify with him or her whether you will be paid say twenty dollars per hour or per each class you teach. If you get paid $20 for each 45-minute-class, congratulations, but if you get paid $20 for every hour you teach, this would be more the norm in my experience as your employer would be increasing his or her profit while you contemplate the universe.
As far as working by the hour or with a salary, weigh what other benefits they can offer you. A good company should state that over-time would be paid at a certain rate per hour.
If you have further questions, feel free to e-mail me or visit me working inside my on-line school and speak with me directly there.
Eric Paul Monroe