Great Teacher Onizuka/Headscratchers

Principal Daimon lacks the authority to fire an assistant teacher on the spot due to the teachers' union contract. Wouldn't that same contract prohibit her from constantly adjusting teacher salaries in real time based on an arbitrary point system?
 * It should, but I've long since given up looking for rationality in this manga.

How exactly would a 13 year old unwed single mother be able to afford an apartment in Tokyo, the world's most expensive city to live in, still make enough to support a newborn, and have time to raise said newborn without any help from her family? Does Japan have the world's greatest welfare system or something?
 * She was 13 when she had him, she's like what, 26 at least now?
 * Support groups, friends, staying in a shelter for years, etc, etc. A lot of things could happen to make this work that are not mentioned in the series. If I can recall, it is never implied that she immediately joined the workforce and began supporting herself and her child at 13, just that that was the age where she had the kid and left her family.

I have a hard time wrapping my head around the idea that Ai Tokiwa would feel up the new teacher's chest just to resolve a bust-size betting competition among the boys. Even after the Onizuka lesson wiped out her "all penis-bearing people are evil" mentality, I would think that she would have some objection to that kind of molestation (and objectification).
 * Compared to Tokiwa cutting Fuyutsuki's skirt short and her panties completely off, then e-mailing everyone at the school about it, her treatment of the new teacher is pretty tame (or at least not malevolent in intent).