This is a deep subject, so I'll try and keep my answers short and to the point (something I regularly fail at. Here we go).
Should "kids" be allowed to play M-rated games online? If they're not allowed to buy them from the store, then probably not. It should always be based on the maturity level of the kid and the supervision and knowledge of the parents, in which case a bright, studious, moral kid may be alright playing it, but that's ONLY with known maturity and parental awareness. Almost regardless of their maturity level, we probably shouldn't allow them to communicate with others over the internet. I doubt any good can really come of that. At even age 13, I was a sore loser. For every year before then, increase my agitation and capacity to be annoying. I was considered mature for my age. Now transfer that to your average kid, and you can see the problems it can present.
Similar story with whether people under age 17 should be allowed to play M-rated games. If they're not mature (hence the rating) enough to understand how to best handle what they experience, they shouldn't be playing it. I'm known as a very peaceful, mature guy, but I can play entirely violent video games and watch movies with lots of swearing and not turn into a gangster because I'm mature enough to know how to process it. I'm not going to try and separate someone's arms from their body or incorporate swearing into my dialogue just because that's how they did it in the violent video games or movies. An 8-year-old with an immature mind who pulls too much inspiration from what he sees, however, may respond differently, and you really do have to watch to make sure they don't try and imitate too much of the negative side of entertainment. If they love the violence, chances are they'll become violent to emulate it.
Eh. So much for keeping my answers short and to the point. At least I've gotten my message across.
P.S.: Funny familial relations, actually. I tend to be a little loose on M-rated games based on my previous statements, but my sister has declared she won't even let her future children play Ocarina of Time (an E-rated game) until they're teenagers because of the blood and spookiness in the Shadow Temple and whatnot. She's made it clear she's adhering strictly to the ESRB ratings at the very least. We kind of grew up on T-rated games and the like, so hopefully her children won't pry into her past too much....