Q1. Do H-1B transfer to the new employer, either a company or school.
Q2. Do H-1B transfer again to an idustrial company and begin to work immediately after filing the transfer petition (get the receipt).
Q3. Yes, you can work part time in a company at the same time when you work in a school, but you need to get a H-1B status from that company.
Q4. If you are very sure that you will be laid off, you have better accept the postdoc position and do H-1B transfer. No resignation is needed in your case.
Also, please keep in mind that total H-1 period is 6 years including working in a school plus in an industrial company. So, please file a GC application as soon as possible.
Q2. Do H-1B transfer again to an idustrial company and begin to work immediately after filing the transfer petition (get the receipt).
Q3. Yes, you can work part time in a company at the same time when you work in a school, but you need to get a H-1B status from that company.
Q4. If you are very sure that you will be laid off, you have better accept the postdoc position and do H-1B transfer. No resignation is needed in your case.
Also, please keep in mind that total H-1 period is 6 years including working in a school plus in an industrial company. So, please file a GC application as soon as possible.