The fields on the Asset Summary page cannot be changed, and some fields will indeed not be displayed if they do not contain any data. You can add extra custom fields to the Asset Summary page though, as explained here:
Similarly, the default Assets tab does not allow direct customization of visible fields. However, you can achieve this flexibility by creating a custom report.
To get started, we recommend using the built-in report "Assets: All columns from the Assets menu" as a foundation. You can then modify it to display exactly the fields you need.