How could I customize the layout of SharePoint Modern site?
Could I download master page for modern site and customizing this by for example a copy?
No, SharePoint Modern site does not have concept of master page. Hence you won't able to directly customize as we used to do in classic experience. You can customize modern site using below options
You might have to go through below resources for other available options.
You have the feature for page templates from April 2019. Here you have the Microsoft article talking about it.
Custom master pages is not supported in modern pages currently.
Quote from the article:
Supported customizations for "modern" pages:
- Custom branding
- Adding "modern" pages programmatically
- Adding, deleting, and updating client-side web parts on "modern" pages
- Alternative layouts
These customizations are currently not supported for "modern" pages:
- Adding "classic" web parts on "modern" pages
- Custom CSS via AlternateCSSUrl web property
- Custom master pages (more extensive branding will be supported later using alternative options)
- Minimal Download Strategy (MDS) -Modern pages inside of the a Site Template package (Save site as a template)
SharePoint Modern Sites requires "SharePoint Framework(spfx) Extensions" in order to extend SharePoint User Experience. It's the modern SharePoint alternative to "Master pages".
You can find official Microsoft Documentation on extensions here.