1) I already yelled a bit about this, so I'll mostly be repeating myself.
http://www.thebore.com/forum/index.php?topic=45437.msg2430445#msg24304452) In both the NYT article and in Peterson's response on his site, he's explicitly proposing this
to address male violence. Even the nicest, softest version of this boils down to adjusting the rules and incentives of dating to steer women towards men they would otherwise not choose, in hopes that those men will be less likely to lash out.
3) Peterson basically ducks the details of how to do this, just saying it would be socially rather than legally. But the traditional way this was accomplished was by excluding women from the economy so they'd be financially dependent on men, and by attaching a very punitive stigma to unwed mothers and their children. Considering Peterson's comments about tradition, women in the workplace, feminism, etc. and the fact that he doesn't offer any specific alternatives, I think it's fair to say those are the most likely options on the table.
4) He's basically accepted and repeated the red pill incel framing of this as male violence being a problem that women are obligated to solve through sex. He thinks that coercing women to do this "socially" rather than setting up a formal government program means it should be a bland, uncontroversial idea and doesn't get why everyone's so worked up.