I had been holding the above-mentioned visa sponsered by an employer. If I resign from my current employer and become independent - as a free lancer or part time in the same field/industry, is it allowed by law or is there anything that I need to be alert of?

I also got married with a Japanese and is going to change the visa to spousal visa soon. Should I let the immigration bureau know at that time that I became independent and earn money through free lance, or would it cause any troubles by informing them? Or would it be better to declare that I am looking for another job in the same field instead?