Hi Magna,
Generally, when you add a custom dropdown field to a table, a screen is generated in your account for adding, modifying and removing the records in the dropdown table. The screen generated will have the same name as the field and can be located under Customize > Screens. You can also build a screen yourself. Have a look at the screen CRM_ActivityStatusList for an example of a screen with similar functionality.
In order to make the field required on a database level, you need to make sure that all records in the table have a value for this field. Once you have done this, you can select the “Required?” checkbox on the edit fields screen for the table.
Additionally, you can make the field required on the screen level. To do this, just add a conditional warning to check if the field is blank when the record is saved. If the field is blank, a warning will be displayed and any actions following the warning (including the save action) will not be processed. The following can be added to the field caption after the text to display the red “required” asterisk.
<span style='color:red' class='pspan'><b>*</b></span>
I hope this helps.
Audisho