In "b" you meant to say "the AF area mode acts like Single Point"...not "AF-S"...and that's right. Also, it's my experience that AF-A never switches to AF-C when the flash is mounted (or even when the built-in flash is popped.)
So yeah...looks like you got it.
I don't think there was ever a question of setting the D7000 to AF-C manually with flash. The question was, would AF-A switch to AF-C with flash. It doesn't on my D90, but I don't have a D7000 to try it. That's what we need to check. But I'm pretty sure it doesn't.
Here's how AF-C works with flash...the AF-Assist light will only come on with the initial half-press. Once your fully press the shutter, you won't get AF-Assist on subsequent firings. Once the flash fires, it needs to recharge. During recharging, your camera will continue to fire shots without flash. Those shots will be useless.
It's possible that when shooting at a very low power, the flash will keep up with your continuous shooting. But that only happens when photographing objects with direct flash (no bounce) that are close to you.