A. Depending on the period until the next visa extension, the actions you must do will change.

If there is only one or two months until the visa extension period, you must start preparing for a visa extenstion application.

The point is that it is not clear the extension is permitted or not for your new company. 
If you change your company, you need the same documents and procedures as you apply for a new visa.

It is necessary to create a document that carefully explains why the company matches your expertise.

And if you have more than half a year upto visa extenstion, you msut start to apply "CERTIFICATE OF AUTHORIZED EMPLOYMENT" instead of an extenstion.

The CERTIFICATE OF AUTHORIZED EMPLOYMENT proves that your job at the company is suited to working-visa requirements or not.
So, if you have this certificate, the next extenstion will be very easy.

In terms of documents, it is the same as applying a new visa.
However, even if an application for a CERTIFICATE OF AUTHORIZED EMPLOYMENT is not permitted, you can listen to the reason for its refusal. And it is useful for exenstion application, so it means that the chances of visa application are doubled.

If you change your company, please get ready to obtain a CERTIFICATE OF AUTHORIZED EMPLOYMENT or extension application as soon as possible.