Going back a few steps, you are saying you see this error still?
Make sure your PHP session configuration is valid and working
That's a fatal error for a reason, and likely something you will need to get in touch with your host for. The setup sets a session var, redirects you to a different page, and checks that session var to ensure that sessions are working on the server. If it can't retrieve the value from the session var, that is obviously a serious problem and it will prevent you from running setup until it's been solved.
In some cases it could be a permissions issue (as you tried but didn't have access for), but it could also be a php misconfiguration. That's not really my area of expertise, so I suggest sending a ticket to the host asking them to check it out and resolve the issue.
Why the one click install worked? Probably cause it doesn't care about errors and has its own methodology of creating a new instance of MODX without ever doing the health checks the setup performs. In case you hadn't noticed, I'm not a fan of those kind of scripts either

The reason the hash was set to MD5 is probably from the way the one click script creates the user. As of 2.1.0, PBKDF2 is the default and newly created users will have those with a proper salt.