After your edit, does your question really make sense to you still? Of course nuclear is non fossil?
And yes, whether we go full renewable or a mix of nuclear and renewable is IMO a second order question, the main focus should be carbon neutral to negative economy ASAP.
Well, only if you are pedantic with fossil meaning long dead organic (which is true, of course). But for energy it makes more sense to distinguish between sources that can be used or they are gone (sun shines on the planet and at some point the heat dissipates back into the universe) and those that are gone at some point because we have used them. So, yeah, point taken, but then I do not think it makes much sense to distinguish between fossil and non-fossil for the point you want make here, which is dependence on a time-limited resource.
I disagree on your last point. By far our biggest problem right now is to keep the climate stable enough. Earth's carbon absorption rate is the most critical resource we have, not the amount of non renewable energy resources that are left. The first problem we have to solve within 1-20 years max., the second is more like 100-500 years (Uranium/Thorium/Plutonium/Fossil Fuel that's available).
That is true, but wind and solar do not change because we do use them, they will occur anew. Nuclear material does not reappear (within our system on earth). So the entropy increases for wind and solar anyways, while much slower for uranium under normal circumstances.
Which comes with the desirable property of solving the problem of radioactive waste storage, as waste is stored in a very convenient place far away from any human dwelling.
Edit: Or non-fossil, if that is a difference