This is a variation on Kevin's answer with the focus on a different part.
Noah had no access to a time travel device and therefore developed his own. The tunnels were available (for some time) but they didn't allow him to travel to where he wanted to go (1920). He used the children as guinea pigs to see if the chair worked, and there were many experiments needed.
There are three ways to time travel: using a device (suitcase or golden ball), using the portal (blue orb), or using the tunnels in the cave.
- By device (suitcase, chair or golden ball), which travels with the traveller
- The portals (blue orb), which stays behind, the traveller cannot use the same portal to return
- The tunnels in the cave can be used by anyone, but they only connect 1953/4, 1986/7 and 2019/20.
In 1920, Adam has a portal device, which Noah uses (in 1921) to get to 2020. From that point on, he stays in that time, working together with Claudia and Jonas.
In 2053, Noah's child is taken and he vows to Elizabth to find her again. He uses the portal in the power plant (the same one Jonas travels through) to get back to the 1953/1986/2019 time period, which is connected via the tunnels.
It's unclear which time period Noah he visits first (unless I missed it), but he is seen pingponging between them. Remember that at some point the Stranger (middle age Jonas) closes these tunnels as well, so Noah is stuck in time without any available portal or time travelling device.
It's important to realize that Noah has no access to time travel other than the tunnels, which means that Noah is unable to get back to Adam's time.
This is why he develops the chair, as it is his only way to get back to Adam. Noah is devoutly loyal to Adam, who seemingly holds all the answers. Therefore, Noah wants to get back to Adam in his quest to find his daughter.
Unrelated to the question, Adam uses Noah's passion to find his daughter to steer him towards killing old Claudia, claiming that the last pages of the book hold the answers Noah is looking for (where his daughter is), but Adam's real goal was to kill Claudia.
The children that are abducted and essentially killed via the chair were experiments to check if the chair was working.
And again, why were these peoples faces being burned off? And what was the motivation for doing it?
It seems like the chair with the metal ring around your head worked but killed the traveller in the process, as it killed everyone who used it (the abducted children) and burned their eyes off, but it did send their bodies to another time period.
But when Noah sends young Helge back to his time in 1953, we see that Noah has developed a new and non-lethal kind of chair, one that is encased in a much larger metal cylinder. Based on the repeated failure of the earlier model, he presumably rebuilt the chair and managed to make that one work.