We applied client's customized master page, then the ribbon is missing some icon. Not sure if it's resolution issue, how should I troubleshoot it?
Number of things you can try here. Revert back to OOTB master page. If it fixes the issue, then obviously the problem is on the new master page.
Security Trimming is the hiding, disabling of data or controls within SharePoint based on the user's defined access.
Hope this helps.