What are some of the ways that databases can be secured so that they can't be hacked into, etc.?
The first level of security is always the OS security level. If you follow good security practices at the OS level, you'll greatly enhance your security. After this, use Informix security to have your users run from an non-Informix password so that you can maintain the proper security on your DBA password.
Also, be aware that Informix's connectivity products will be operating on a user-specified port. You need to know whether or not your security scheme adequately protects you from such port-based intrusions.