From what I've seen, a small saw, whether it be Leatherman, SAK, or even a simple wire saw, makes it possible to take down surprisingly large trees. They give you the ability to create a fault plane and then apply main force to finish the job. IME, the strength of a tree is mostly of the outer third of its diameter. A small saw (or a small and sharp knife, wielded with skill) punches far beyond its weight.

In terms of sustaining a reliable fire, I suggest that regional differences apply. There is no simple rule. In my part of the world, putting three 12-in. logs over a bed of coals would almost certainly fizzle in a most inconvenient way. We (obviously) have to adjust our techniques to the materials at hand.