Is the battle distance realistic?

Mind you, at 50km the vanilla designs aren't that effective. That's when the engagement starts, not necessarily when it's resolved, which usually happens closer to 20km, depending on the weapons used. 

Missile and drone carriers are great until they run out of ordnance. They are good (just like in today's naval warfare), but at the same time, the same type of weapon that makes a great missile defense also tends to make a great ship killer due to sheer volume of rounds it puts out. If a ship doesn't put some of its reactor power into close-in defense, it might be in for a nasty surprise when something does plow through its missile swarms. Guns are making a comeback on modern warships for similar reasons (that, and shore bombardment, which is very expensive to do with missiles), but it's actually easier in space because the guns generally have a longer range.

Mind you, thermocouples we are using are highly exotic. It might be possible to generate efficiencies we have, but osmium, for example, is extremely expensive. Turbines are used in powerplants because they're much less expensive. In general, civilian power plants are not a good match for reactors that we use, and even naval ones are not mass-optimized (they go for volume optimization instead). Optimal COADE reactors actually run on very low thermal efficiency in order to have smaller radiators, a concern not shared with any terrestrial reactor. We won't see loops that hot in terrestrial designs because they aren't needed nor wanted, and we're not using weapons-grade uranium for the same reasons (though we probably could).

If you want to pyrolyse CO2 in a nuclear reactor, you need a completely different design that would be optimized for generating high temperatures this requires. It's a nice idea, but not actually optimal for power generation (although it could do that on the side, of course). We also don't currently have any reactors of that type. Building a new type of reactor is a long and expensive affair, I'd say a carbon tax would actually get better results faster. That said, at the rate things are going, we're going to need sequestration anyway.

Yeah, we optimize for volume because less volume=less mass to a degree, but take a look at what the reactor size actually is. The thermocouple is the largest part of COADE reactors, the actual reactor vessel is rather dinky, especially if using weapons-grade fuel. It's also where the mass is, but I'm pretty sure a turbine designed to run in those conditions would weigh a lot, too, even if you made it out of amorphous carbon. Of course, turbines being heavy doesn't bother a waterborne ship, so it can take the mass penalty. Turbines are also cheaper than huge chunks of osmium and tungsten, which is a big factor in the real world.