Hi @damirakz,
Would it be possible to set only one image there? If I want it to be statical?
Yes you can achieve this by attaching slider category to only one post that you have set featured image.
Also I read that header image is not resizable. But as I attached the picture from Sparkling theme example there is full screen header image, how could I do mine as well like that?
You have to just set larger images as thumbnail images for the slider posts and then regenerate the image thumbnails using the following plugin.
That it would be the same for all screens?
The slider displays only on home page but if you want to display it on other pages also then you can use the custom child theme shared in the following reply.
https://colorlibsupport.com/t/slider-on-every-pages/#post-47733
Best Regards,
Movin