Freelancing on Student Visa

Posted this in r/movingtojapan but it was recommended to post here with the tax questions.

Hi, I need a ELI5 explanation regarding the nuances of freelancing and being on a student visa. I am so sorry if this is repetitive, there are so many subreddits, and so many different answers that I feel more comfortable asking on my own.

I am coming to Japan in October for 1 year, on a student visa for a language school. Coming from the US. I freelance, every now and then.

Here is what I have gathered:

1. I need the "permission to engage in activities…….." on my visa allowing me to work up to a maximum of 28 hours per week on a Student Visa. I have this filled out already and plan to have this form with me when I land at the airport, or do it online before if I can, but will probably wait.
2. Something about a sole proprietorship? Will I need this as a student? I feel like doing this screams I am more concerned with work than school, which isn't the case. I just need spending money for being a girl and wanting my nails done, and maybe like going out and getting drinks.
3. Time tracking is essential, which I like to do anyway, so I have no problem with this.
4. Taxes?? I have read I might need some help for this, but basically paying twice (US and Japan)? Maybe? Or just filing in the US that I am in Japan and reporting what I made and paying taxes in Japan? help.

Situation: I freelance through Upwork, never more than 28 hours a week (I never even apply to full-time roles)and it varies when I will have a contract or not. I am active sometimes, then inactive others. Right now, I have a client who advised they may need me for some one off projects, that will take about 20 hrs per month, sometime within the next 3 months. For this same client, I usually do about 8ish hours of work and am compensated about 29,000 yen ($200 usd) to do it on an as needed basis monthly. These projects would be separate from that, and the time with the client will be up in 6 months.

Questions:

1. If I do not currently have a contract at the time I land, and I get my permission, how do I notify them I got a contract for a remote company? I read they would want this when it's not in the general permission, but if I don't have this how do I go about that post permission and notifying them?
2. This will at max generate $700 USD a month, on good months, if not, $200 is standard. Is there a max or something I can make while there?

I would like to keep it legal, obvs, and of course I want to try to find work IN Japan, because this isn't long term or consistent so the permission is valid, just concerned about freelancing. Any advice is helpful 🙂