Great questions. I have wrestled with a lot of these myself. I think Block’s abandonment paper and Kinsella’s article How We Come To Own Ourselves are important here.
I have written about some of the more practical concerns here. Some of your questions are addressed there. I’ll address the others here, not point-by-point, but by explaining how I see things.
It’s important to remember that political philosophy is about avoiding/resolving conflicts, and conflicts have two parties. In the case of abortion, in all issues relating to very young children, and in many issues relating to older children, the conflict is NOT between the parents and the child, but between the parents and some third-party taking it upon themselves to “stand up for” the child. It is useful to bear in mind when we’re talking about a conflict between adults about a child, and when we’re talking about a conflict where the child is one of the parties to the conflict.
It is also important to remember the limits of ‘armchair’ philosophy. Take the homesteading principle. The libertarian can give a general idea of what practical steps must be taken in order to establish the necessary objective inter-subjectively ascertainable link between the first-user and a previously unowned object such that he can be called the homesteader and first-owner, but the libertarian cannot be too specific. For example, what are the necessary practical steps that must be taken by a man who wants to homestead a field. Is a sign enough? With a fence? How about ploughing the field? When has enough been done, exactly, for him to have legitimately homesteaded the field? The libertarian can give no concrete answer, except to say that the ‘boundary’ will be drawn by the courts, in cases of conflict, i.e. where two parties are claiming to own the same field. It is the very nature of applying theoretical principles to reality that some things will be ‘arbitrary,’ in that there’s no particular reason for where the boundary is being drawn. Where courts are private, where they draw the line will be ultimately be determined by the customs of society, where consumers in general believe is the appropriate place for the line to be drawn.
Libertarianism can be boiled down to the homesteading principle, but the abandonment principle is just as fundamental. Homesteading and abandonment are really two sides of the same coin. Just as you can have conflicts over what exactly constitutes homesteading, you can have conflicts over what exactly constitutes abandonment. And the boundary line will once again be determined by courts based on custom, and can only be arbitrary. Take the example of a newspaper. A man dumps a newspaper in a rubbish bin and five seconds later another man takes it out and claims it as his own. But the first man turns round and claims that he had not abandoned it, he had merely placed it there temporarily, meaning to return to it. He accuses the second man of theft. Here is a case where a court must decide whether or not the first man’s actions constituted abandonment. They must decide whether the second man is guilty of theft, or whether the first man is guilty of forestalling (preventing the homesteading of an unowned object).
One more example: take a field which has been neglected for some time, and the owner cannot be found. When does it become acceptable for someone else to start using the field as their own? Not one day, that would be simple trespass. What about a year? 10 years? 100 years? At some point, the field must be considered abandoned, even though the owner has not actively abandoned it. The courts might draw the line at 5 years. Then, if the owner of the field comes back to find someone else is now controlling and claiming ownership of the land, he is out of luck. The land is no longer his. His actions, or rather lack of actions, constitute abandonment of the field, so the new owner was homesteading unowned property, not trespassing. This means that ownership must be actively retained by taking certain actions, or else it will be considered abandoned. It would be accurate to refer to this as a positive obligation, though that term is often associated with something else entirely. It would be accurate to say that the owner of the field had a positive obligation to not neglect his field for five years, if he wanted to still be considered the owner of it.
Now to the subject at hand.
I take Kinsella’s view that a child acquires rights to “own themselves”, i.e. rights to decide what happens to their bodies, gradually through childhood. “Growing up” can be thought of as the process of a child acquiring more and more rights to their bodies, as they develop and start using their body faculties, until they are a “grown up” or full self-owner. From our armchairs, we can say that at conception the new “body” is fully owned by the mother, and at some point (probably during teenage years) the new body will be fully self-owned. There may be conflicts between the child and the parents. This can be interpreted as the child accusing his parents of forestalling (preventing him from acquiring new rights to his body) and the parents accusing their child of trespass (invasion of rights that still rightfully belong to them, for now).
As I said before, abortion is not a conflict of this sort, but a conflict about the child between the mother and some third-party. The court must decide who is the rightful “owner of the child” out of these two parties. That is, the court must decide which of the two parties owns the rights that the child has not yet “grown into” or homesteaded. That is, which party owns the parenting rights, or rights to “raise” the child, or, more precisely, the right to selectively exclude others from providing support to their child.
Just like all ownership rights, there are certain actions (that may be called positive obligations) that must be taken if these parenting rights are to be retained, and there are certain actions that constitute abandonment of parenting rights, meaning the parenting rights become unowned and available for homesteading. In my post I referred to the most obvious case calling for abandonment of parenting rights: child abuse. I showed how a court might award ownership of the parenting rights to a third-party rather than a clearly abusive parent, by taking the view that the abuse constituted abandonment of the parenting rights, so if the abuser refused to give up the child to a third-party, he would be forestalling, or preventing the homesteading of unowned property.
In the same way they decided 5 years neglect constitutes abandonment of a field, the courts must decide what constitutes abandonment of parenting rights, i.e. what actions justify the parenting rights being awarded to someone other than the parents. (Naturally, it will also depend on who that third party is; close relatives who are willing to take in the child will be given preference over unrelated parties, and if there are no related parties, the unrelated parties will be strictly vetted.)
This is the framework I use to view disputes relating to children. I think most of the problems you raise in your post can be solved by looking at the subject through this framework.
I question whether the analogy is close enough to the real scenario to be relevant. To make it more accurate, I must come into existence for the very first time during the helicopter ride, and the ride must last 9 months, during which time I’ll be kicking you and consuming a considerable part of the nutrients of your body. Now, I would not necessarily think it unethical for you to push me out the helicopter and retake control the first chance you get. You would be ending a kidnapping situation, the only way you could. I think this analogy is closer.