I'll do my best to answer. I've worked on rad shielding, but that is a different side. If acidburnNSA (a reactor scientist) shows up, ask him, he frequents nuclear posts. These will be basic answers so I hope they help and I'll expand on them if you want to follow up, but there's a lot to cover just in the first paragraph.
> What's the long term storage costs for spent fuel rods?
Not too much. Frankly because the quantity is low. This is one of the things people don't realize, while the waste is highly contaminated there's REALLY small quantities. We're talking about less than a coke can of waste per person per year. (that's not per reactor, that's ALL reactors) It is expensive though. The cost of nuclear is from construction and decommissioning. Operating costs are extremely low.
> Is this factored into the price?
Yes (mostly)
> Is post plant cleanup factored into generation costs (we're paying for a nuclear plant closing nearby in our electric bills now on top of generation costs)?
Yes (mostly)
Mostly means that it is supposed to be factored in. But those are of course estimates. I'll also be honest that sometimes people cheat.
> Can we possibly reuse those spent fuel rods for something else useful?
They already are. 17% of France's electricity is from recycled nuclear. That's not 17% of France's nuclear energy, that's 17% of TOTAL energy. Additionally most of these materials are used for a lot of other things. A lot goes to medical.
> Can we prevent disasters like Fukishima?
Yes, actually Fukushima is a great example of how to prevent disasters like Fukushima. The reactors that didn't fail had their backup generators on higher ground. There were also better safety factors and I'm over simplifying things, but the reactors that failed had sub par safety factors. We've had much better designed reactors for awhile, but that's a longer conversation and extremely convoluted (you'll commonly see it expressed simpler, but nothing is simple).
> Can we prevent every single disaster?
No. Such a notion is really unrealistic. I'd rephrase it as "Can we reduce danger to an acceptable risk?" Which I'd say the answer is yes. I'd even say we've been there for awhile. Nuclear fission is, next to hydro, the safest form of electricity we have, even when you include predictions of future deaths from past events (Chernobyl and Fukushima).
> (an implied one) Can we reduce environmental damage from meltdown events?
Yes! Actually this is super interesting. Chernobyl has turned into a really big nature preserve. Wildlife is thriving there. It is interesting to also look at radiation maps of Japan [0]. For context to this map, all measurements are in nSv (1e-9Sv). 1Sv within a year equates to a 5.5% increase in chance of cancer over your lifetime. But 20mSv is the max allowed dosage to a radiation worker. You'll notice that the vast majority of places is WELL below the 20mSv mark. Max value I found was 8,528nSv/hr (82528nSv/hr1e-9(Sv/nSv)24(hrs)*365(days) = 74.7mSv/yr). The point of this last part isn't to say something like "oh well humans can live here hur dur dur", but rather to illustrate why Fukushima is turning into a nature preserve. But I do also want to acknowledge that many people did lose their homes and have been permanently displaced. Again, I believe that we should be honest.
> Thorium reactors...
This is a convoluted subject. I'll leave it for another post. There's (a lot of) potential but we definitely need to do more research and testing.
> Fusion reactors...
Are a completely different beast. They don't have the same radiation concerns. Their waste product is mostly Helium (a resource we are in short supply of). While fission and fusion are both nuclear based there are more differences than similarities (including power output, by orders of magnitude). Think like the difference between nuclear and coal. Both heat water to turn turbines (this is how almost all electricity is generated actually), but they're very different in most aspects.
> We already had one problem by not thinking about long term negatives...
Honestly this is why I'm PRO nuclear. Sure it has negatives, and I'm not going to try to deny them. If we're considering human lives then consider that coal kills an order of magnitude more Americans per year than have ever died from Chernobyl (several orders when you consider the world). We also have to consider the places that have become uninhabitable because of mining and other things that humans have done. Everything has negatives, I think we're just more aware of nuclear's (fission's). It is about the exchange of good and bad and if we net more good than bad. It is also about comparing to our other options. (If we're in a negative sum game we are trying to get the least negative, but we're still getting negative utility) I won't dive into this because it seems you're aware of this. It is honestly complicated and a difficult subject. It takes a lot of research. But there's a saying "When it comes to nuclear, those that know the most fear the least." There's a reason that the majority of climate researchers are pro nuclear, there's a reason the UN Climate Committee endorses nuclear.
> I really want to avoid contamination of the only planet we can currently live in as a species.
I'm with you there. 110%. We're hundreds of years from being able to live somewhere else. We must do everything we can to protect THIS planet.
Again, I'm happy for a follow up and I will do my best to answer.
[0] https://jciv.iidj.net/map/