Regarding your roommate’s job, the short answer is that it’s almost definitely illegal. Even when there’s no work permit violation (which there usually is), you can still be fined if you’re not properly qualified in the eyes of the government.
Traditionally, the perception has been that the tax office doesn’t communicate with the offices that would arrange for you to be arrested, fined and deported. Recently it has been claimed that that is changing.
If you want to “go straight”, there is apparently no benefit to turning yourself in. Just quit your illegal job immediately, never work illegally again, and ask a lawyer what you should do about your taxes.
If the school (presumably a buxiban) has actually been reporting your income to the tax office and not just pretending to do so, you should eventually (by January or February next year) receive proof of this; the withholding statements will have the appropriate stamp.
The purpose of claiming its “income from professional practice” and not “salary” is presumably to avoid the perception of an employment relationship and whatever scrutiny might accompany it. (Either that or it’s a convenient excuse to take an extra 2% of your pay – or both.)