Hi,
1. With the "dynamic display" activated, the filter will only display the values selected in the products displaying on the current products listing. Turn off that setting and it will display all the values you entered in the custom field.
2. The filtering system is not adapted to dates. The date system in custom fields was added after the filtering system was added to HikaShop. So I would recommend to break the date into three dropdown custom fields for the year, month,day selection and have three filters in them so that it would then do something usable.