No, it doesn't have anything to do with heap-vs-stack, if that's what you mean.
That would be the greatest lower bound, and just one possibility for 'a. Of course, somewhat the one that matters the most, granted.
Sounds correct.
At least for me, a little more explicitness ...
There's just no one-size-fits-all. I, too, would have gotten into it better if it was very exact, maybe even with a formal definition or something, even if that meant tough reading upfront. But I'm pretty sure that would not have been optimal for most other people.