I'm using asp.net 4.0 and MySQL. Last week my hosting firm changed security level of from full to medium. MySQL connector doesn't work correctly anymore. For this reason I'm using old version of ADO.net MySQL connector version number 6.2.5.
Does this situation make my site vulnerable for any attack?
The MySQL Connector 6.2.5 is the latest version. I don't understand why you think it's an older version. Your problems of appending values to your queries and not using prepared statements (if you're doing that) are way more than the version of the connector you are using.