Three very interesting questions!

1: Gods are born primarily of belief in them. They are also born of worship and rituals. Old Gods are born from religions and folklore, which is a mix of worship and rituals. The ancient cultures all had their religion, their myth and their traditions, and it is from this specific worship the gods are born. If one singular person just believes in something, however, it cannot work. The belief needs to be a mass belief, and the ritual widespread, for the gods to actually exist. This is why they are beings of religion, mythologies and folklores, not just one singular belief (else everything we believe in would be true).

This is the same for the New Gods. The Spooks for exemple are born of the widespread conspiracy theories (belief), while entities such as the gods of technology are born of ritualistic worship (sitting in front of a computer at regular hours, while "offering it" things like time and attention and effort, or praying for computers or the Internet to work - in themselves small, insignificant things, but when widespread and done en masse, enough to create a form of god).

2- Thor is Odin's biological son, yes. But he is also a god.

The gods can have children between themselves... in their homelands. In their respective mythologies. Thor, like all the other Old Gods, was born out of belief (here the belief that he was Odin's son) and came from his mythology and religion.

3- How come Odin and Demeter couldn't have a child? Now that's easily explanaible.

I will remind you first that season 3 has several time shown to be inexact and weird concerning the lore of AG, contradicting the novel or even previous seasons.

In the novel, it is clearly explained that the Old Gods (hear American version of the gods, we do not know much about the original gods in Europe, Asia, Africa) can rarely have children with mortals - it is exceptional, most of them being sterile. As a result, half-gods such as Shadow Moon are truly a miracle. And so far, the two half-gods we met in the AG universe (Shadow and Fat Charlie) are born of a male god impregnating a female human. It seems to be the only way for the gods in America to reproduce.

The fact Odin and Demeter had a child in season 3 is, according to the novel's lore, impossible (and I guess it is why it wasn't viable?). In the AG universe the gods are born from belief, worship - the Old Gods specifically are born from legends and myths of their homelands. The gods only exist because they exist in culture and tales. As a result, it is impossible for two gods to create a new god all on their own, since nobody believed, worshipped or told the tales of the "son of Odin and Demeter". So even if they wanted, in the novel they wouldn't even have a baby at all.

In fact, the baby's existence as a being of flesh and blood cannot even be explained, by anything in the lore of the novel or of the previous seasons.

So yeah... if the baby was a divine entity (which is the only option since it wouldn't make sense for two gods to birth a human), it could not survive because it belonged to nothing - it wasn't believed in or worshipped. It did not exist in either Demeter's or Odin's respective mythologies and thus couldn't be created. That's the best explanation I got

So when a god is born, he or she only materialize or first in spiritual form?

A god can only be born if people believe and worship him or her.

A god cannot exist if there is not a legend or a worship associated to them. The Olds Gods are born out of their mythologies. Thor could only be born of Odin because legends, mythologies and religion said that he was the son of Odin.

So yeah, the gods are before anything manifestations of belief and worship. A god or goddess can probably have a child with a mortal because it is natural, human reproduction, of flesh and blood. But two gods cannot birth a "god" alone because a god is only born of worship and belief.

(But again, the child of Odin and Demeter is a VERY confusing thing, especially since it is never specified what it is or how it could have been conceived. There is nothing anywhere in the novel or previous seasons about such a topic).

But yes, a god exist primarily as the manifestation of a belief or a worship.

Gods are born from thought so Thor is only Odín’s son because people believed he was and Odin and Demeter’s child died because she was never believed in and the reason Shadow lived was because of his human half

Technically speaking you are right, but for the Demeter child the problem is even more complex - and reveals one of the big troubles to the writing of season 3 - because if nobody believed, worshipped or even invented in a legend or a myth the idea of a child between Demeter and Odin, the child probably couldn't have been conceived at all, period. There wouldn't even be a stillborn baby.

It is especially jarring when you actually compare it to the "biology" of the gods in the novel, where it is clearly explained that gods do not worry about having children (at least the Old Gods) because they have an extremely low fertility (if not inexistent), and can't reproduce with each other - hence why they can only have children with humans, and even then it is a one in a million type of chance to have a baby. But yeah, to create a human you don't need an entire religion or superstition to form, while it is what creates the gods. Hence why it is strange, by logical point of view, that this baby could even have been formed because if it was a divine baby... then it couldn't exist without a legend/belief/folklore/myth. It is the basic of what American Gods is about.

No worship or belief = no god. Not even a baby god.

The idea is not that gods first exist, then because people believe in them they are shaped in their personas, attributes and powers. It is the reverse: a god only exists if people have already an idea, a belief, a role to give them. Gods do not exist as blank canvas for people to draw their gods and demons on - and thus a "blank canvas" like this baby can't logically exist. That's why there is a hole in the logic of season 3.

And maybe they decided to go against what the novel established in term of divine biology, but the thing is that they never mentionned or explained it, either in the episodes or in behind-the-scenes content (like interview or official BTS material).