Cutomize Sharepoint Online Branding

Depends on the Site Type you are working on. Options below

1. Team Site template (group template or classic team with modern page) - No full width layout (even if you set page layout to Home from Article) unless do some CSS wizardry to hide the navigation. Know that MS is constantly changing the page structure for modern pages, so if you are using Hard Coded CSS hierarchy references they might break. Also, will not work with All pages only the pages the web part is put.

2. Comm Sites - Comm sites come with Full page layout, so have to worry about Top navigation. So this is the safest option but again the list and libraries will have Article layout.

Regarding publishing sites, if they are classic they are still in use.

Regarding page layouts, don't know if anything maps to page layouts in Modern sense, you can always use Sections (modern page) to rearrange your content but doesn't give the full flexibility of Grids (Bootstrap or Office Fabric). If you need that flexibility, then create a Giant web part with your layout and deploy it to the page.