shynung

I'd imagine there would be balance problems. Imagine holding a wide object while walking on a fence.

The Soyuz rocket family are transported to its launch pad in Baikonur by train, fully assembled. The central core was tapered to make room for the side boosters, so as to fit the train's maximum load dimensions.

For that purpose, only a single yo-weight is used. The asymmetric yo-weight release would induce the spent booster to tumble, provided it was positioned correctly.

AFAIK, in mining, explosives are used to break a chunk of ground into small-enough pieces that the diggers can scoop up into the trucks. So, use case for a nuke mining bomb would be to blow open the side of a mountain, to access the ore within.

Is it possible to make a megaton-class nuclear bomb that doesn't leave radioactive fallout? Say, for mining purposes.

The projectile is already mostly plasma after it goes through the frontmost plate. Slowing down small, high-velocity fragments are what aerogels are good for. Aerogels also have very low density, so putting on several meters thick of it would not give a significant mass penalty.

Best to fill the space between the thin plate (Whipple shield, I presume) and the main armor with some sort of aerogel. It adds additional mechanical resistance to the rapidly-disintegrating projectile/debris, giving it a chance that it may never reach the main armor at all, stuck inside the aerogel. Also, it's a good idea to stick a layer of fibrous armor (like aramid/Kevlar) just behind the main armor, to catch any spalls. Also a good idea is to angle the armor, to increase its effective thickness (a projectile impacting armor at an angle has to go through more armor compared to one impacting straight). Also, angling the armor gives the projectile a chance to bounce off instead of digging into the armor.

Is this level of maneuverability even possible? Say, with drones or missiles?

It is, it's called an air-augmented rocket. Still uses internally-stored fuel and oxidizer, but takes extra propellant from the surrounding atmosphere. It won't approach turbojet levels of efficiency, but pretty close to LH2-fed nuclear thermal rocket.

I'm thinking of a gas-core fission reactor (think nuclear lightbulb) with the fusion fuel snuck into the fuel loop.

Is it possible to build a hybrid fission-fusion reactor design? If so, how would it perform against standard fission reactor designs?

I read that this trick was put to use in the SR-71 spyplane. Some of the outer skin, in particular the chines along the side of the fuselage, are cooled by the incoming charge of fuel.

AFAIK, on a rocket engine, regenerative cooling was done to keep the nozzle and chamber from melting despite the vigorous reaction happening inside them.

So, like regenerative cooling, but being used to generate heat instead of cooling the chamber/nozzle. I don't think putting a turbine past the HX would do much good. That would sap propellant line pressure, and it's needed for thrust. Much simpler to plug a generator at the turbopump shaft instead.

Well, yeah. NSWR is still sketchy as it is. Mostly because there's no one ballsy enough to test it out. Project Orion nuclear pulse rocket at least had small-scale test models using conventional explosives. Well, OP seems to be concerned primarily on ISP, and not much else. FFRE is at the higher end of ISP performance, so that's what I pointed out. Of course, OP has found out about Slough's magneto-inertial fusion rocket independently. So that's that.