for space age, this turned out to be very unbalanced in my opinion, reactors take up very little space on spaceships, plus they do not need refueling automation at all, also because of more powerful installations they are easier to transport to other planets, I would suggest increasing the weight of installations so that they cannot be transported at all in rockets, also and for kernels (dangerous cargo)
, Realism is cool, but not everything in the game is realistic, so it ruins the current balance

You've echoed some of my own thoughts about this, so expect an update soon, probably today, that is consistent with your points, at least about the weight of reactors and turbines.

When I was looking at weights for the 1.8.0 update, I noticed that while uranium fuel is massively over-weight in the base game, but also, as you point out here, that reactors are massively underweight, relative to their ingredients. Reactors specifically are simply set to be able to move 1 reactor per launch, whereas the weight of the concrete alone should take 5. And, I didn't look at the weight of heat exchangers and turbines when I made them more compact and more expensive.

Weights in Factorio are jank in general. Never mind realism, they are not even consistent with each other. For example, there are places where it is possible to use productivity bonuses to produce more mass in product than was contained in the ingredients. And of course, uranium is just massively overweight in general.

Now, by this mod's very concept, being overpowered on purpose is not out of the question. And unburned nuclear fuel is actually quite safe, even by real-world standards.[1] But with reactors and the rest of the power plant, balance, realism, and consistency actually point in the same direction, which is to make everything else much heavier.

[1] Of course, by Factorio standards it's even safer. What's the worst that could happen, the rocket explodes and showers the planet's surface with enriched uranium? That's where the uranium came from to begin with, so it's not even really pollution if you think about it.

when I wrote about dangerous cargo, I meant that it is necessary to remove the ability to transport cores in missiles, and make the damage heavier, thereby complicating its transportation

I don't know what you mean by "make the damage heavier".

Core, that's what I mean.

weigh down the uranium

Version 1.9.0 makes nuclear reactors, heat exchangers, and steam turbines much heavier, and makes heat pipes slightly heavier. Aside from heat pipes, these will now need to be assembled on-platform to use in space.

Cores remain the same weight. Conveying the extreme energy content of nuclear fuel is a central point of this mod, and on that point, balance is a secondary priority. However, with everything needed to actually use it being much heavier, they are now just one of many other items that will need to be launched into or produced in space to use nuclear power on a platform.

I haven't reached fusion reactors yet, but doesn't your mod make them useless? At first glance, it seemed to me that they were less powerful, but I did not experience it.

Maybe. This mod was first made in 1.1 and didn't consider fusion at all, so while it doesn't directly change them if might make them worse by comparison.