How can I set a custom lead field’s type as date?

The custom fields in MailBluster are designed for string data types.
It is not designed for date and time. So you can only store text in the custom fields of MailBluster.

As for the Standard Segment, you can use Type as Date added:

Create segment from Standard Segment

These are the options you will get in the Operator:

Selecting Operator from Date added

You can set the conditions in the segment based on the lead’s adding date to MailBluster.