New sole propietorship (eikaiwa) with one employee

So I inherited an eikaiwa last month, and I have one employee who works under 20 hours a week. When it comes to running a business in Japan I’m a fish out of water (in terms of the paperwork and procedures).

I’ve already registered the business, and have been through the first month of income and expenses. Other than the registration, and tax filing in December, are there any other commitments and/or forms I need to fill out and submit?

I need to submit a Kyuyo Shiharai Jimusho Tou no Kaisetsu Todoke with my local tax office I’ve been told so far, but I’m trying to make sure everything is squeaky clean.