Residence status change, student to spouse of Japanese national – can I still work while waiting?

Hi there, as the title says – I'm currently on a student visa. I applied for the residence status change in October and am in the waiting period, and from what I understand, it's taking a few months these days.

I graduate from my language school at the end of December. I'm expecting that my status change may not be completed by then – but, I've been offered a part-time job to start in December.

I have the permission to work, but the time I leave school, I know the school will notify that I'm no longer enrolled.

A. While I'm waiting for the status change, do I have to notify them that I've left my school?

B. Can I still work my part-time job while I wait?

My current zairyou expires in February so there should be enough time, but in the mean time… I definitely need to be working.

by Venture_compound