Freelancer for foreign firm w/o ties to Japan

Hi, I moved to Japan from Germany on a spouse visa. Before moving I quit my job with an IT-company in Germany. I now have the chance to resume this job on a work-from-home basis (albeit only part-time). However, this would be as a freelancer with me billing the company for my work, rather than being a regular employee.
I did some research on the internet, but some things are still not clear to me. It would be great if someone in the know could give me hints towards my issues:

- Would in my case the registration as a sole proprietor be sufficient?

- Can I bill in Euros and in English language? My plan is to to so and then have an Excel file where I list all the billed amounts and convert them into Yen per the day of the invoice. The sum in Yen in a year would then be my income for all taxation purposes.

- What about VAT? The company only operates in Germany, has only German customers and nothing to do whatsoever with other countries, let alone Japan. Is VAT something that I have to consider at all when issuing an invoice to the company for my work?

- Could there be any other issues with me writing invoices to a foreign company? I found online-templates for Japanese invoices which I would use. Also there seems to be a new invoice system being implemented in Japan in October 2023. Is there anything I have to consider regarding this?

Again, it would be great if someone knowledgeable could give me some tips. That would help me a lot!

Thanks a lot!
Matt

You can bill them in any currency you want. Just convert it and pay your taxes in yen.

Same for GST. Bill whatever amount is correct. Pay the extra taxes in yen if applicible.