About public schools in japan

It depends upon your lifestyle, the city where you gonna plan to move as Tokyo is very expensive in terms of making apartment contracts. You need to have a Japanese guarantor (either an individual or a Japanese company) who takes responsibility for your financial problems. International schools are expensive as well. You could expect at least 100000 JPY for one kid at the elementary level.

For a moderate life, it's enough but if you prefer brands, it would not be enough.

For health insurance and other stuff, I think you have to pay by yourself for every individual monthly unless your company doesn't provide family support.

You need to also have the Japanese language to have a better life here. Without Japanese it's quite challenging to survive here as you can't easily find a replacement job as most of the companies will require you to speak Japanese.