No idea what happens if the commander gets killed. If it's anything special, I've never noticed it.
As for how I schedule my training, I've tried 3 things:
All year training, 7/10 minimum present - This generates some enraged / depressed by long patrol duty unhappy thoughts, but it never seems to make the soldiers less than quite content. The key is having enough happy thoughts to balance it out. Letting the soldiers sleep in their own bedrooms and having a good dining room seems to be plenty for me.
One month on, one month off, 7/10 minimum present - So, the idea is that dwarves train half the year and are off duty half the year, in alternating months. This has the problem of causing "complained about the draft" and "upset about being relieved from duty" unhappy thoughts in some dwarf pretty much every month. Dwarves that are peasants will be unhappy at being relieved of duty, but based on what I've seen, are still upset at long patrol duty.
Despite my fears that this would cause lots of unhappiness due to the above issues, it doesn't seem to be that bad, since it theoretically avoids long patrol duty. Not always though, which I suspect is caused by the occasional siege where they're on duty for a few months to finish off the invaders.
Two months on, one month off, 7/10 minimum present - This is what I'm trying now. Two months of training followed by a month of inactivity. The theory is that it will train faster than the above method, while avoiding the worst of the long patrol duty bad thoughts. I haven't tested it well yet, but it doesn't seem to be annoying the soldiers unduly.
In the end, I really have no idea if it's even possible to completely avoid unhappy thoughts related to scheduling. It's just best to mitigate the damage with happy thoughts. I also have no idea just how much the X/10 minimum present requirement helps or hurts this. I think it'll mostly help with avoiding dwarves idling around waiting for demonstrations because half of their squad is asleep. Not sure how much it helps or hurts happiness.