#2 (which seems to be a consequence of #1 - check it's text!), doesn't, either (!)
It doesn't seem to be implied as a consequence to me. "All coexistence battles" can well stand for "all zero of them".
The reason why they're in a numerical sequence is because their order is important, stacking limits are only enforced after any coexistence battles are fought, so no coexistence battle's odds are influenced by stacking limits. The numerical list is used in all other instances of such ordered sequences as well, as far as I can tell. The steps per round on page 14, the various steps during setup on page 13, the draw orders phase on page 16, etc. etc.
A bulleted list on the other hand is used in the rulebook to denote alternatives, like in the action step you pointed out: The player can do either. When it comes to the two steps of the change initiative step, that's not the case: First the first step is carried out, then the second step is carried out. And nowhere in the second step is it implied that the first step had to include more than zero instances in "all coexistence battles".
So I'd argue that not only are they sequential and not consequential, but also that a numerical list is the only reasonable way in the context of the rest of the rules to denote this.
I think the rules for Hero Abilites are generally spelled out under the Engaging Units section (pg.25, first paragraph under the header). Looks to me that once a Hero is engaged, his abilites "kick in" (become active).
Hm, it doesn't seem that clear to me... although I wholeheartedly agree with you that it makes sense to use their abilities right when they're denoted as being engaged in the battle, the text doesn't mention this. On page 25, it always talks about "units and heroes", never about heroes alone. Page 26 only explicitly talks about drawing hero cards - which is a common hero special ability, as page 32 makes clear.
Even then, their unique special abilities would have to trigger before the common special ability in order to influence the battle concerning how many combat cards are drawn. I already mentioned that one of these unique special abilities (Khan's) has to trigger earlier or it doesn't really make any sense at all, so it makes sense that the others do as well, but the rulebook just doesn't state this.