Rent-a-Body

If this was my world I would play it like this:

(1) There are temporary bodies you can download yourself into whenever interaction is needed with the outside world. These might be androids, vehicles, spaceships, construction or mining equipment. Whenever something is needed to service the central server, these temporary bodies are used.

(2) There is little incentive to raise a child in a purely digital world. You don't get that same attachment to a newborn baby. You might as well simulate that attachment.

(3) Uploaded people live for thousands of years before they succumb to circuit decay, or voluntarily end their own lives. So there is little need to create new people.

(4) If you upload a baby's mind it never properly develops. Or rather it adapts super well and evolves to to "the next paradigm" of human development. This is looked down upon by the current less evolved generation.

So how does childbirth work?

(a) You apply for a childbirth license and register a lease on a bio-android body. Essentially a synthetic skeleton with organs grown in and around it in a vat of chemicals.

(b) You can either select a given genetic code or use the one assigned to you in the central database. Either way you get a sense of attachment to the new child.

(c) Procreate and have a baby.

(c.5) Some people do the procreation artificially, and only wake up the android shortly before or after the child is born.

(d) Raise the child to maturity in the real world.

(e) Upload the young adult into the server.

(e.5) During their upbringing the child can make trips into the central server. This lowers the shock value at age 18 where their biological body is obliterated and they are permanently uploaded. The parents can also switch bodies as appropriate.

Question: How does this change what a "household" is? Of course it removes any need for male-female parenting teams.

Who says they have to be new? Take a copy of an existing person at random. Strip off the memories, the training, go back to the very core of a person - congratulations on your new child.

In your world, people are digital - we can copy without loss. We don't have an upper population limit.

Frankly, we (including top neuroscientists) have no clue how conscious works, what it is exactly, where it comes from, and how to make new ones (except the biological way).

Asking if a digital consciousness could have children is therefore impossible to answer (without wild speculation). The only reasonable guess we can make is that a digital consciousness would be able to make copies/clone itself.

Really, it's up to the plot of whatever story you're writing but if you have computers capable of simulating a human consciousness, simulating a sperm and an egg and the subsequent digital-biological child shouldn't be too difficult. Sure, that's a lot of cells and you'd need a virtual environment to "raise" the child in but it would be doable.

Yes - the Ghostborn

The way you describe them, for your infomorphs you are following the dichotomy of emulated uploaded minds ('Ghosts' - digital equivalent of naturally-evolved neural networks) and true artificial intelligences ('AIs' - programmed intelligent software or artificially designed neural network, with or without some layers of network 'evolution' on top of that, but not made by copying any naturally-evolved ones). That means you have the technology for the former, and you can expand it to emulating more than just adult brains.

It will be more CPU- and memory-intensive, as you will want to emulate the embryo's whole body to account for all the complex procedural influences required for the formation of a brain the 'normal' ways (but in emulation). It also will require sufficient prior research into human development - a lot of it. But given those two parameters, it's not physically impossible to emulate the whole process of growth from a single cell, just very computationally resource-intensive.

I don't recall the concept explored often in fiction, but I have recently found that Greg Egan's Singleton does have it as a major part of the central events, and the concept is also present (but taken for granted, without as much novelty or focus, since the this story is set millennia after the events of Singleton) in his Schild's Ladder.

Who maintains the virtual world's infrastructure? They can fertilize embryos.

If every human being is biologically born and then uploaded at birth, someone or something has to service the computers. If that someone or something is human, then there should be a human population capable of producing the offspring that get uploaded. I don't think that's what you're looking for, though.

My understanding is that your world has virtually zero adult humans outside the system. That's a problem, because something still has to keep the computers running.

You may want to build a mini-society composed of robots capable of sustaining the internet. When parts fail, spares will be manufactured and installed by automated drones. When you run out of spare parts, raw materials will be harvested and refined by mining bots. Plus, you will need someone to service the dozens of power plants that keep the system online in the first place.

You can employ some of these robots to conduct in-vitro fertilization. They can fertilize stored eggs with stored sperm, provide sustenance to developing embryos in artificial wombs, and then harvest each consciousness at the right developmental stage. It can be fully automated like the Matrix - except the bodies are composted.

One problem with this solution is that you will eventually run out of eggs and sperm. You may need a factory-sized genetics lab in which DNA is constantly recombined and distributed into lab-grown gamete cells. In this way, parents in the virtual world can have biological children.

Yes

An uploaded mind is just a program and you can copy programs and make new programs.

A parenting program would take random features from both parents and build a base personality matrix from that. Said parents could then take the new AI and teach it just like a normal child.

Considered everyone is an AI, making a new AI is no difference.

In the Matrix, Sati is a child program of two other programs.