You can quickly turn the "unknown" card into a lead or contact. Simply click it and you'll see the two options: create lead, create contact.
If you click a lead or a contact card you will see its snapshot view - a quick summary of all its Salesforce data.
For a contact you'll be able to easily navigate to its Account snapshot view. In the top right corner there is always an icon/link opening this record in Salesforce.
The snapshot view shows all open activities and activity history right away under the 'ACTIVITY' tab and you can quickly create a new task or log a call from there.
You can switch to the 'DETAILS' tab to see all lead/contact details or to 'RELATED' to see related opportunities and cases. Click any of the related cards and you'll be able to see their snapshot views too.
Account snapshot view:
Opportunity snapshot view: