Will not update – can not remove earlier version

You seem to have issues around permission settings.

https://www.ads-software.com/support/topic/updates-not-working-3
https://www.ads-software.com/support/topic/unable-to-set-up-child-theme

Better to ask your host support to check your server configuration.

Would the permissions setting affect only the Contact 7 plugin? All other plugins are updating without issue.

Also, if it is a permissions issue; 1) could that be what is causing the forms to not send? 2) What are the necessary permission setting to enable the form to send and to delete or update this plugin?

**Note** The forms were previously working fine. I last tested them in September.

I don’t know. Contact your host’s support.

You could try to delete the plugin folder at wp-content/plugins/contact-form-7/ using FTP (don’t use Delete option on Plugins page as this may erase all CF7 forms) and install the plugin again.
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For file permission issues see https://codex.www.ads-software.com/Changing_File_Permissions.