DDE's have the ability to reactivate an Identity record by adding an academic affiliation using Manage Affiliates. They can only reactivate those who are in the department they are a DDE for.
The person you reactivated needs to renew their account by using Identity Manager. They need to go to im.ucsb.edu, select Manage Identity, select the proper affiliation, enter the required information and "Begin Identity Activation".
Yes, for example, if a student employee gets an empID then leaves and comes back 2 years later as an employee, the employee ID remains the same.
If someone was an academic affiliate for another department, their Sponsor Department needs to be updated. You can submit a ServiceNow ticket to have that updated.