Hi Joseph,
The enrollees are currently only displayed on the edit page for the event. We plan to add the ability to display enrollees on the detail page in the next version and add some extra functionality for admins. I have added your requirements to the item on Gemini - EVT-7227.
The names of the custom fields can be modified under Admin/Languages/Language Editor. Select Local Resources/Desktop Modules/Events/App_LocalResources. There are a number of views they are displayed on, but you should find them all in that list.
The custom fields are per event at the moment, not per enrollee, so could not currently be used for an anttendee to fill in as they enroll. Perhaps you'd like to detail your requirements for this on Gemini, and we can look for inclusion in a future release of the module. If you submit an request via the DNN Core Feamework and Modules [Public ] project, it will get picked up and moved to the events project at some point.
Cheers
Roger