Explanation
The root cause of why the CustomField__c field they added to the entity has no values under the header in the CSV file output is that the user does not have rights to the custom field. A user's access to a field is determined by their profile and permission sets, which define their field-level security settings. Field-level security settings control whether a user can see, edit, or delete the value for a particular field on an object. If a user does not have access to a field, they will not be able to view or modify its value in any interface, including Data Loader. Data Loader is a tool that allows users to import or export data between Salesforce and CSV files. When using Data Loader to export data from an org, Data Loader will only include fields that are accessible to the user based on their field-level security settings. If a user does not have access to a field, Data Loader will not include that field in the CSV file, neither as a column header nor as a value. The developer does not have the correct JDK that is recommended by Salesforce and this is known to cause issues with exporting custom attributes is not the root cause of why CustomField__c has no values under the header in the CSV file output, as it is not related to field access or Data Loader functionality. The developer does not have access to the object's metadata is not the root cause either, as it is not related to field access or Data Loader functionality. The object's metadata defines its structure and properties, such as fields, relationships, and layouts. The field is not populated is not the root cause either, as it contradictsthe fact that CustomField__c has no column header in the CSV file output. If the field was not populated but accessible to the user, Data Loader would still include CustomField__c as a column header in the CSV file, but leave its values blank. Salesforce References: Data Loader Guide: Export Data from Salesforce, [Data Loader Guide: Field Mapping],
[Salesforce Help: Set Field-Level Security]