Hey, i think its not a good idea to post various different issues within a single thread. Often this brings confusion into such a thread and then you won’t get that much answers or solutions.
Personally i would suggest to do the following:
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Manually update to 10.0.9 without using the updater app (this should also solve the integrity message when done correctly).
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Configure your web server to serve ownCloud via HTTPS (this should also solve the 404 not found issue as your web server is providing different content via HTTP and HTTPS).
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Fix your web server configuration according to https://doc.owncloud.org/server/latest/admin_manual/configuration/server/security_setup_warnings.html#your-web-server-is-not-yet-set-up-properly-to-allow-file-synchronization (this should solve both WebDAV issues).
Once those steps are solved i would suggest to create a new thread for each remaining issue.