Custom master pages is not supported in modern pages currently.
Quote from the article:
Supported customizations for "modern" pages:
Adding "modern" pages programmatically
Adding, deleting, and updating client-side web parts on "modern" pages
These customizations are currently not supported for "...
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
Create Application customizer to add header and footer on page.
You can create modern custom pages and select layout like one column, 2 column etc...
You might ...
First try adding Full/Absolute URL of icon as below:
<SharePoint:SPShortcutIcon runat="server" IconUrl="https://sharepoint.com/sites/abc/SiteAssets/images/Logo48x48.png" />
If it is working then try adding relative URL like this (If icon is stored on top level site: https://sharepoint.com):
<SharePoint:SPShortcutIcon runat="server" IconUrl="/...
What we would do is use default page context info attribute ...
There is a tricky solution:
You can add a webpart to a page normally, in a webpart zone.
In this webpart you can specify the css style to display or hide any element you want.
Finally set target audience to this webpart and everything will work as expected.