Is your mysql server running on your dedicated server? Check your my.cnf to see if "skip-networking" is uncommented. Comment that line and restart your mysql instance and see if that lets you in. Check 'ps aux' to make sure it's running after the restart.
As for 'is it secure', one would hope
If you haven't secured your box, you may want to secure it before opening more ports to the world. For more info on securing this type of setup, post/search in the Linux - Security forum, we really have some security guru's living over there.