Is it obligatory to pay the remaining amount to a teacher who failed to fulfill her commitments in a beauty course, knowing that she did not teach the trainees sufficiently, seized their belongings, and threatened them with unforgiveness?

The woman must fulfill what was agreed upon in the ijarah (leasing/hiring) contract. You must pay the agreed-upon wage, as it is a binding contract. The hired person is entitled to the full wage once they have made themselves available and have not refused to work, even if the hirer rescinds the contract before the agreed-upon period, unless there is an overwhelming excuse.

You are obliged to pay the woman her wage as long as she is ready to complete the course, and she is obliged to return any of your belongings she took. If there is any deficiency on her part, the wage can only be reduced in proportion to that deficiency. It is advisable to continue the course and agree with her on a solution for the issue of slow benefit.

As for her not praying and committing forbidden acts, this does not affect the validity of the ijarah contract. However, she should be enjoined from evil deeds and commanded to repent.