only in home page I would like to be with logo and icons white with transparent background and when I scroll down it becomes as I set it up on the editor (just sure it’s shorter in height)
The main factor for header height is your logo. There is empty space in the image above and below the actual picture. You should be able to crop it in Shopify admin via “Edit image” button.
Crop as tight as you can – theme adds some vertical padding anyway…
For the homepage I’d like it to be transparent only on the first hero banner and the when I scroll it comes back to the original set up (white background and black logo and icons).
I just want to ask you whether it’s possible to put the icons a logos in white instead of using invert (the main color is dark grey so it does not change to white but to light grey).
Also, if possible use the same rule for mobile and tablet.
In my solution above I’ve suggested a particular way of adding this code to your theme – in a “Custom liquid” section added to the homepage template.
Exactly because adding it to a Template area will only render this code on a page using this template – on homepage only.
If you add it to a layout/theme.liquid, it will apply to every page, so some conditional logic will be needed.
And most important – if you edit theme code it will make further theme updates much more complex.
Whatever you do in Customizer, will persist through theme updates.