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This is Tim with Microsoft Office 365 SharePoint Support.
There are multiple ways to edit your public-facing website. You can append the URL to your website with /_layouts/wh/Editor/default.aspx to launch the in browser editor.
You can use the Edit Website link in the Administration Portal.
You can also access the pages editor from your Team Site.
Please try to use these options and let me know if you are still seeing the issue. If you are, please let me know exactly what happens when you try to edit your website.
Microsoft Office 365 SharePoint Support