Of course if you assume continued exponential growth you will run into limits. The correct response to that is to not assume continued exponential growth indefinitely, since in the real world that never happens.
In actual real world systems, the growth curve is sigmoidal: it starts out with exponential growth, becomes linear, then asymptotically flattens as system constraints are approached. This is already happening with human population, and should be expected to start happening with other resource curves in the fairly near term. Any properly grounded analysis would look at the situation from this point of view.
The exponential growth of neutron flux in a detonating nuke may be overwhelmed by a different function as the pieces fly apart, but I wouldn't want to be part of that even allowing for it being a metaphor.
wrong. As system constraints are reached, growth becomes negative. In other words, you need a steady supply of resources just to maintain existing stuff.
No, you don't, because "resources" don't magically vanish once you've used them. They just become harder to extract (assuming they're not already being renewed--in the biosphere, "resources" are constantly being renewed by biological processes); but that's what technology is for. For example, it is said that we are using up fossil fuels; but combustion processes don't need "fossil fuels" specifically, they just need easily transportable liquid fuels with decent chemical energy content, and we can make those, because the atoms that the fuels are made of are still there; they didn't vanish when we burned the fuel. We don't do that now because it's cheaper to use fossil fuels while we have them; but of course that will change as fossil fuels run out.
Similar remarks apply to just about anything we currently call "waste"; sooner or later, if we need to, we will find ways to recycle all of that "waste" into something usable. The key limitation is population growth, but as I've already said, population growth is already into the "asymptotically flattening" phase.
It's possible, of course, that population growth will in fact go negative (many projections assume that); but that doesn't mean it will stay that way. The exact sigmoid curve is obviously an idealization; real world systems do oscillate about reasonable equilibrium points instead of just staying stuck at them.
In actual real world systems, the growth curve is sigmoidal: it starts out with exponential growth, becomes linear, then asymptotically flattens as system constraints are approached. This is already happening with human population, and should be expected to start happening with other resource curves in the fairly near term. Any properly grounded analysis would look at the situation from this point of view.