All right, after death in space, we should also talk about birth in space. Is it possible?Technically, yes, but we have a long way to do.
It is not easy for a highly trained, super healthy astronaut to deal with the differences between space and earth, much less for a newborn baby or later, a child. While growing up, its eyes would get puffy and its face would swell up because the gravity doesn't pull the fluids down like it does on earth.
The child would experience deformities of the bones and the muscles. Astronauts prevent this by strict exercise. You have probably seen that the ISS had exercising equipment like in a gym.
As if the deformations and swelling are not enough, the baby / child would also be exposed to high radiation.
All in all, space isn't a good environment for babies or children at this time.
For reasons we'll all understand, no experiments involving babies or children in space have been done. Mice born in space have proven to be very disoriented and have problems with balance when arriving on earth,
This issue has been discussed to death in some space-oriented Facebook groups. Everybody with an ounce of common sense seems to agree that having babies can wait until the colony can support the extra population. This is partly because babies will consume resources without contributing anything to the colony at first. This mostly just means that irresponsible behavior will have to be penalized in some way until people just get used to the idea that the entire colony could collapse if a "whoops" happens too often.
You are right that a baby that is born in space could have health problems, too. There's been suggestions that prospective colonists should be screened for recessive genes that could cause serious birth defects in a child and colonists with a harmful recessive gene might have to agree to be sterilized before they can join the colony. It's not really eugenics; it's an acknowledgement that the space colony won't have resources like a full-service hospital that can save the life of a child with a serious enough birth defect. That means the problem will have to be prevented from the start if at all possible.
One question comes to mind here. What if the space colony has no ties with earth, at all. How will they keep existing? The current colonists would get old eventually, and die, and there would be nobody left to continue.
In a way I can't imagine that a space colony would sever all ties with earth, unless something happened on earth and nobody survived. In that case, being able to reproduce would be very important.
On the same note, what to do with the elderly? Just like with babies and young children, the elderly, when they get very old, would also consume resources without being able to contribute. I was curious enough to look it up but found very little about it. I'm sure it has been discussed, I just can't find much about the subject.
Those are good questions. I would imagine that ties with Earth won't be severed for quite a while yet, at least not until the colony is capable of not only being minimally self-sufficient, but also thriving and expanding on its own -- or until a disaster happens on Earth, in which case wise colonists would look out for the colony's interests. Even then, again, the colony will have to use common sense and not do anything that would threaten the survival of the colony as a whole. That includes having more children than the colony's resources are capable of supporting. The best way to handle it, I suppose, would be to force both the mother and the father to take responsibility for the existence of the child, including having the mother and father take on extra work to make sure that the resources are being created to support that child.
As far as the elderly and those who somehow become disabled and can't work are concerned, it will also be a matter for the colony to decide. Making tough decisions like this could make the colony look brutal to those who are cooling their heels back on Earth. Sometimes you just have to leave somebody behind so everybody else can survive. In ideal situations, though, colonists would have the equivalent of a "living will" in which each one decides what happens when and if they become unfit to work and a burden to the colony. If you ask the Aspiring Martians Facebook group, they could probably tell you what they think.
Working