please give us more information about your environment. Which Redmine and MySql Version is at the moment installed on the Server?
The problem with:
“Authentication method ‘mysql_old_password’ not supported by any of the available plugins..”
looks like a very old Version of MySql, see the following link:
The mysql_old_password plugin implements authentication as used before MySQL 4.1.1 that is based on shorter password hash values. For information about this authentication method, see Section 188.8.131.52, “Password Hashing in MySQL”.
Could you please update your MySql Server to the current Release
(Current Generally Available Release: 5.5.28) and migrate your Database for testing?