Before I respond, these are great questions, and I do not propose that I am a libertarian spokesperson, nor an expert, but a fellow researcher like yourself. So with that in mind, I look forward to your responses to my responses to your questions, as I think we can eventually squeeze out some gems from this back and forth, but it might not be a quick process.
Each one of those topics has a subtle difference to the overall idea of self ownership.
First, if we are to assume the Libertarian umbrella, I believe we can safely assume a minarchist mindset, which still includes the trappings of statism. It may be a more subdued and less intrusive form of the State but a State non-the-less. So from that view point, I will address your argument (as apposed to a strict Anarcho-Capitalist view point).
– Parents and children disagreeing over whether a child is ready to be “on their own”
As there is a State, there is a “legal age” in which a child is still the financial liability of the child’s parents and/or guardian. The child does not own its actions, as it is not financially liable for them. If it were to act violently in a crime, of which it can be proven the child acted in full knowledge/understanding that their actions were violent, they may be tried as an adult (that would be up to municipalities/individual States).
– Custody disputes
Since the child does not posses full custody/responsibility of their lives until legal age (i.e.- 18 years old) they are the responsibility of two parents in the case of custody disputes. It should be a 50/50 split unless one can be seen as dangerous to the child. It would not be automatic given to the wife (just using a nuclear family in this example. Check tumbler for the 700 new genders which exist now – *sarcasm font*) and it would not be given automatically to the parent of greater means.
– Rights and self-ownership of the developmentally disabled
“Does someone have the legal obligation to take care of someone who cannot take care of themselves who have reached legal age under a libertarian umbrella?” is more the question.
If they are disabled from birth, the parents have been legally responsible for this child for 18 years. Kicking this person out of their house onto the street would result in this persons potential death (different degrees of probability here depending on many variables). This hearkens back to the idea that if you push someone into a lake and they are now drowning you have a responsibility to help right that wrong, but if you didn’t push someone into a lake you do not have a responsibility to help that person, as you did not cause the harm to begin with. I am not suggesting that someone born developmentally disable was harmed intentionally or unintentionally by their parents, but that the parents do take a calculated risk in having a child, and part of that is the state of how the child is born.
– Rights and self-ownership of the mentally ill
First, there needs to be a mechanism to determine “mentally ill” (voting for Bernie based on sound economic policy comes to my mind – *joke font*). But society/state would need a body which decides when someone is mentally ill and is a danger to others. Not themselves. They own their body and can do what ever they want to themselves. If they are mentally ill and want to stay a hermit and eat nothing but frozen pizza’s and watch Fuller House that is up to them. If they want to try and kill the neighbor lady with the left over frozen pizza for making him watch Fuller House, which was just voices in his head telling him to do so (but it could have been self defense as Fuller House is a terrible show) then the local hand of the State would have to get involved in order to keep that person from harming others. If that person becomes mentally ill later in life, after being a self directing member of the country since the legal age (18) then they are responsible for their actions, if they have always been mentally ill, it gets a bit grey – many variables here including being mentally ill and falling into your last question. But lets say they have the voices in their head like the pizza dude/Fuller House, but they have it at age 12. I kind of think the parents are obligated to help their child, and it would be in their best interest as they are legally/financially responsible for their child’s actions.
– Rights and self-ownership of the mentally incapacitated (e.g., loner in a coma)
Generally, the beneficiary or person with power of attorney would have the ability to make legal decision on behalf of someone in this state, much like the courts have now. If that person was married, the spouse has this right under contract law (I believe). If they are not married, the next of kin would be my next reasonable guess. Any express written instructions would have to take president, and would direct the family and any legal guardianship over the body by those written wishes.
– Rights and self-ownership of elderly with dementia (with or without aggressive tendencies) – You always retain rights. A unborn child has a right to life while it is imprisoned in the mothers womb. It can not act on its own, and it has no idea of where it is, what name it has, who is president, who is running (lucky them), and an even worse case of dementia than an elderly person who might even retain the memories of yesteryear. I would argue that once you hit legal age and are not the liability of anyone you are always in retention of self-ownership, even if your mind has dementia. Kind of like my response on the mentally ill applies here.
While I am in two masters math classes at the moment, I do not have a lot of time to dive into the texts to find great “reference this” and “reference that” points, but I was hoping to at least get a dialogue started, as these topics interest me as well.