Well, speaking from experience in the Japan 2011 earthquake, you are kind of on the mark kind of not.
b) it won't really work in major natural disasters, because, well in order to maintain the density of devices, a large number of people need to have continuous access to power, which is unlikely if a disaster is so severe that communication infrastructure is offline (I imagine celltowers are less fragile than power lines).
After power was turned back on, I, and a lot of other people, went out and bought a hand-cranked USB charger(also doubles as a flashlight and radio, a handy device to be sure). It doesn't take that much energy to power a cell phone.
As for the tower issue, the towers where I was at(Tsukuba, which is about halfway between Tokyo and Fukushima) all kept power even after the quake but since so many people were using their phones to either call people or check the news it was almost impossible to get through(the bandwidth of the tower may have very well been degraded as well). A mesh network *might* have been useful there, but it would have had to have enough density to work. Really the biggest problem with using a mesh network for disaster is that anywhere you have enough people to support a mesh network, you could probably just as easily use a bullhorn to communicate.