A high-N braid is a good way of putting it, if I understand what you mean correctly.
Each offspring requires three parents, but they are not required to be distinct (the same parent can be the Mother, Sage, and Dowager). When that happens, one birth slot is consumed, but three new birth slots emerge (on the new alien).

A normal birth (three distinct parents) consumes three birth slots, but three new birth slots emerge. So the total possible birth slots is gradually increasing (depending on the incidence of non-distinct births, which will decrease in frequency over time as the probability of hitting it 'accidentally' decreases

As to the first question, yes of course. Any active player action would immediately reset player status to "active".

At launch there will be only "active" and a rudimentary "passive mode" that we will gradually upgrade over time and then add the toggle into "Sunset" and "inactive" modes only after "passive mode" is fully featured. ("passive mode" is more like a background feature that helps active players keep their THREE flowing in semi-strategic ways)