What is our Shadow...

Eporem

What is our Shadow, if when separated from the Living, the Living become this....

Vevvev

Your shadow once separated also leaves you with the inability to cast spells as seen with the Clockwork City Prologue. You can speak to the woman again in Arteaum and she tells you what it's like to live without a shadow. In the Summerset Trial, Cloudrest, if you or a group member dies in the battle with Z'Maja your shadow is ripped from your body and forced to fight your allies as a thrall under the Sea Sload.

As to what a Shadow is it seems to be the effect you leave on the universe and there is a whole line of magic dedicated to manipulating it. Shadow magic is very powerful and is mostly linked with Nocturnal and her followers, but some cunning mortals have been able to figure it out as well.

Can read more about it here.
https://en.uesp.net/wiki/Lore:Shadow_Magic

Eporem

does it seem as well from this, that our Shadow is a part of our Soul? - The consciousness?

https://en.uesp.net/wiki/Lore:Souls#Vestiges

It is possible that souls are composed of various parts and influenced by variables that are yet to be understood, for example a Shadow of the soul can be separated from it and transformed into an independent entity, leaving original soul in a weakened state.

This_0ne

https://forums.elderscrollsonline.com/en-gb/discussion/577275/what-does-sotha-sil-mean-by-multiverse-in-the-summerset-chapter#latest in the neighboring topic also raised the issue of shadows, including the night blades, so you may be interested