Effectively all out nuclear war in space a century from now, here is how it plays out.
Improving the weapons means we have upped the killitivity coefficient by switching to purely fusion driven weapons, maybe a miniaturized Z-machine to light fusion of hydrogen. How really doesn't matter, the fact is they are fusion weapons and will likely even have a dialable yield. So the world leaders will go for broke and turn that dial to 11 so the maximum yield may very well be multiples of the Tzar Bomb. Which actually will have little effect on the EMP production because you can only ionize the ionosphere so much, according to my EM professor 100kt or 1Mt makes little difference.
As stated, massive global HEMP's could be disastrous in its own right for sure. But the world of 2100 is a little different than our own. Computers have gotten smaller and are thus more susceptible to electronic noise so they are also better shielded and have greater redundancy built in, as a result, may fair better in an EMP. Also, (hopefully) advancements in nanotech would allow for SOC devices to have their own repair mechanisms and/or naturally resilient circuits. For larger infrastructure we may have gotten around to actually protecting against Solar Storms which will serve to protect from the E3 Pulse. Additionally, seeing that it is somewhat of a troublesome time it's fair to assume that EMP resistant infrastructure may be mandated. So it may very well be reasonable to assume that the EMP's would not do much damage.
Purely fusion weapons would have little to no fallout, unless they were designed to. At the altitude stated little radiation from the blasts, if any at all, would make it to the ground because of the atmosphere. Without knowing the yields of the weapons other effects may include: blindness, extreme weather from localized heating (which at the altitude stated would take enormous weapons or high concentrations of detonations).
All satellites/space stations in LEO are probably toast as a direct result of the blast effects. Stations with polar orbits may fair better, but if the actual engagement is occurring in LEO that's a very bad place to be. As a result of the distance and improvements in EMP resistance things in higher orbits should actually be okay during the nuclear strikes.
After the action the Van Allen Belts (especially the inner) would see an enormous increse in radioactivity because the fusion bombs liberate plenty of particles. Things/people not extra rad hard would not do well against that. There is also what is left of the fleet itself; presumably many thousands, if not millions, of tons of vaporized ship that would be blasted into all kinds of orbits. Effectively sand blasting anything it encounters. It would also help deorbit things by increasing drag and probably interfere with radio signals between earth and space. For items not vaporized, you now have hyper velocity shrapnel to deal with and of course, the remaining wreckage of the ships.
Most people on Earth, probably okay. LEO will be hazardous for years and require extensive clean up before it is safe. Beautiful night skyies because of nuclear detonations, auroras, and falling spacecraft.