Path Doesn't exist?

You can check whether the sites are set to basic auth. When you set them back to integrated, SharePoint Designer will be able to open up the sites.

 

Here is a similar thread for your reference:

 

http://sharepoint.stackexchange.com/questions/18006/sharepoint-designer-unable-to-open-web-site

Please refer this article for the issue:

https://blogs.technet.microsoft.com/asiasupp/2011/06/12/error-message-your-client-does-not-support-opening-this-list-with-windows-explorer-when-you-try-to-open-with-explorer-on-a-sharepoint-document-library-in-office-365-site/ 

check if you have proper permission:

 

Go to Site Permissions > Permission Level in ribbon > Click the permission you belongs to > Ensure Use Remote Interfaces is selected.

 

https://social.technet.microsoft.com/Forums/en-US/a0ead2f3-c9c2-4437-b96d-354d4cbda89b/sharepoint-online-2013-cannot-open-in-sp-designer-2013

 

or check this one: https://social.technet.microsoft.com/Forums/en-US/cf2d82bc-4f69-4b9b-a3be-b935abb8bbf3/cannot-open-sharepoint-online-site-with-spd-2013 

Hi check below errors

 

Reason 1: file or folder-level security

Reason 2: view filtering

Reason 3: required metadata and check-out feature

Reason 4: content approval feature

Reason 5: search indexing

Reason 6: moved

Reason 7: deleted