HTTP requests "\x80z\x01\x03\x01" in my Apache logs
Solution 1:
That looks like someone trying to connect using SSL to a non-SSL port (i.e. https://).
Either the connecting clients are getting something wrong, or perhaps your web server is listening on port 443, but not for SSL connections?
You could create an Apache customlog using %p somewhere in the output, and track which port those connections are actually turning up on. If they're on port 443 then your config is potentially the issue, if they're on port 80, I'm not sure what to suggest.
Solution 2:
It looks like someone tries to connect via ssl to non-ssl port.