How can i investigate what duration a specific checksum had when it was sent out
The checksum is not stored in the database, have a look at CRM_Contact_BAO_Contact_Utils more specifically at the methods generateChecksum and validChecksum.

The genereateChecksum method returns the checksum like $checksum_$timestamt_$life the life is in hours, so for a given checksum you could tell when was generated and what was is expire date.

The validChecksum method takes the $contact_id and a $checksum  And validates it. This method is called when a profile/contribution/event/etc page is rendered and is taken from the requested URL.