Although some have reported differently, I've noticed that Marksdwarves will do sort of standard training, as in the stuff that's mostly good for melee, if you set them to a training location/barracks (like a cabinet or a weapon rack or whatever) and schedule them for training. With only the target assigned to them for training, and with no active order, I've typically seen more consistent archery practice, which increases the more-relevant Marksdwarf skills. But, like I said, YMMV. (I may have this wrong, and it might be best to have them scheduled to Train but only have them assigned to a target. I can't remember... I don't use Marksdwarves that much.) Having the Hunting skill enabled on your militia archers may cause problems, or it may not.
Alerts refer to two things: civilian burrow restrictions, with can be set on the Alerts screen, and militia schedules ({s} on the main military screen, I think). Inactive defaults to having no active orders for all months, while Active/Training is "Train" for every month. When you enter the schedules screen, you can see the Alert that you're looking at by looking at the very top bar, which is easy to miss. There's a button to change between different Alerts, somewhere on the schedule screen.
And then there's minimums, a setting that is on the individual order screen, after you go in to change one on the schedule. Having high minimum training numbers, at least for melee-type squads, can cause a slowdown in training rates, as the dwarves in the squad will sometimes seem to prefer doing big demonstrations instead of actually sparring, and will often wait around for a long delay because everyone isn't ready to start yet. I have squads of 3-4 set to 2 minimum training, and I see adequate amounts of sparring, which seems to increase skills faster than demonstrations.
Still, military training will be slow... it's not you'll get everything right and then you'll have everyone hitting Legendary like they're Miners in soil. Better equipment, particularly full steel armor and sharp weapons (silver blunt ones), will really help with the survivability of your militia, even if they don't show it in the skills. Field training on crundles and moose and camels and whatever's wandering around your map can help a bit, as well.