Short term visa and Business Activity in Japan
Assumed that a non-resident of Japan hopes to come to Japan and hold a seminar and receive a fee from attendance.
He will come to Japan with a short term visa or from visa waiver country.
He does not have status of residence (Legal address) in Japan.
In this case he cannot receive fee from such activity based on Japan.
Even if he receives fee after he returns to his home country, as far as it is based on activity in Japan (he holds a seminar in Japan), his activity is illegal.
So legally speaking, he needs to obtain status of residence in Japan.
In order to obtain status of residence (work permit) of Japan, he needs to find a employer in Japan and apply for COE and legal address in Japan.
He may not have intention to live in Japan though, without legal address in Japan, he can not engage in business activity and receive fee.
If he holds a seminar in Japan for free of charge, he does not need to obtain status of residence in Japan.
(However, there should not be a such person.)
If he does not receive fee according to seminar in Japan, but he receives fee from activity conducted outside Japan, it is legal.
Buying items with short term visa of Japan
Assumed that you come to Japan with short term visa or from visa waiver country.
And you buy cosmetics and export them to China and make a profit.
If scale of your purchasing is not large, it is fine. But if the scale of your purchasing is large, you need to acquire necessary status of residence in Japan.
Assumed that you (non resident of Japan) hope to purchase cosmetics from Japan. So you asked your friend who is living in Japan as a language teacher to purchase cosmetics and send them to you.
You paid some remuneration to her.
In this case her activity is illegal. Because it is outside her status of residence in Japan. Actually some persons were arrested. facebook