The water source is used only for cooling; the heated steam is condensed and fed back into the reactor in a closed loop. While cooling is more difficult in space than on Earth, it’s not impossible.

All sources of power require some amount of mined materials, even if its just in construction. Nuclear waste is much less problematic than CO2 emissions, and nuclear power has the advantage of providing a consistent base load.

Is a catastrophic, world-ending feedback loop likely based on what we understand? The IPCC reports paint a grim future, but I don’t believe any has suggested that it’s likely the entire Earth will be rendered completely uninhabitable to human life.

If a system is poorly understood, then by definition it cannot be factored into predictions. When we say something is “unlikely” we mean “it is unlikely based on what we understand”. I don’t think it’s very useful to ask, “Well, is it unlikely based on what we don’t understand?”, because that’s not a question that can be answered.

No; at least, that’s unlikely. But parts of the world that are currently habitable will be made inhabitable, and biodiversity will continue to fall. We’ll likely see more extreme weather events, increased migration from areas that are too hot or underwater, and issues with global food supply. Coral reefs may completely disappear.

However, progress is being made, and while it’s not as quick as we’d like, carbon emissions for modern economies like the US and EU are on a downward curve. In 2021 EU’s carbon emissions were back to pre-1967 levels, while the US’s carbon emissions were back to pre-1979 levels (Source). So there’s cause for hope; the worst thing we can do is give up. Everything we do now lessens the scale of the problem in future.