Can't install plugins
It would be nice to know for sure, so we can throw pertinent errors to the user.
Maybe manually check the data/other/plugins.xml and see whats in it. Maybe rename it and try again
Are you having issue saving pages ?
Does the other folder have an htaccess file if apache ?
My host was once in read only filesystem mode, but permissions said everything was fine. But writes actually failed.
My goal is to make health check as robust as possible to catch all these issues.