Custom data fields not showing on event registration page
You will need to add it to whatever profile your using for the event registration page. You can check what profiles your using by going to the online registration tab of event configuration. Once you know which one then go to administration -> custom data and screens -> profiles and edit the fields for the particular profile. 

The other thing you will need to make sure is that if your wanting anonymous users to submit the form they have access to the custom data. This can be done via 1. CiviCRM's permissions granting them access to all custom data or by adding in a rule into Civicrm's acl permissions that everyone can edit that custom data. 

Seamus