You gave me a lot to think about. Tackling the main one that I think maps best to the situation at hand:
> Let's say this process takes 40 weeks, and at about week 10 the neighbor says "I don't want you in my house any more -- please leave". Should the neighbor be allowed to say this, even if this means the formerly healthy person will require daily dialysis, and may indeed die?
I would say no, there is at least an implied contract with such severe consequences for backing out that it cannot be backed out of without it becoming murder (it would meet mens rea).
> What if the neighbor themself has suddenly developed kidney failure, no transplants are available, and the only thing that will save them is an immediate 30-week stay in the special room?
This one maps to the mother's health, which will almost always be prioritised (though I'm sure there are exceptions/considerations depending on circumstances). I reckon this is done for two reasons, that an adult is a known quantity whereas the child may be born and still not make it, but also because the mother can probably try again. In the case of the room, if the room would continue to work its magic even though the owner died then I'm not sure society/law would prioritise them.
It might also map to a doctor treating someone in hospital then falling ill themselves.
> What if the neighbor's own infant child has suddenly developed kidney failure, no transplants are available, and the only thing that will save them is an immediate 30-week stay in the special room; should they be allowed to evict the recovering kidney donor?
This one was difficult but I'd have to say no, based on the same reason as above, that the treatment had started and there was (at least) an implied contract to finish it and knowledge to not to would be reckless and akin to murder.
In the UK the House of Lords ruled[1]:
> that it was lawful to withdraw life-sustaining medical treatment from [a] man who had fallen into the condition known as permanent vegetative state. Their Lordships agreed that although, in withdrawing the life-sustaining treatment, death would be intended, his death would not be regarded at law as caused by the withdrawal of the treatment, but rather by his underlying condition.
(I've edited that for consideration to the family and length)
That decision was considered controversial among the medical community (apparently[2]). However, I doubt one could justify withdrawing treatment to someone who would probably go on to live a full life.
> If the neighbor is just being selfish
No.
> One way or another, if the room is empty at the end of the 40 weeks, should the state use eminent domain to seize the room
No. Property rights mean something (to me, anyway), and in our analogy that would be like the state making someone forcibly pregnant or available for rape. That's not the same as telling someone who became pregnant through actions of their own free will to bear the ultimate responsibility for those actions, nor forcing someone to keep to a contract they made freely.
> I have found that some things may be wrong to do, but society should still be structured in such a way that people may sometimes do wrong things.
I agree, which is one reason why I'm against abortion but pro-choice (because it would go against bodily autonomy, so I choose the lesser of two evils). I'm not against quite short term limits.
[1] https://academic.oup.com/medlaw/article-abstract/13/3/357/94...
[2] https://pubmed.ncbi.nlm.nih.gov/15991403/