Connect contact (or potential) to lead post-conversion

Using the "Converted Leads" view I can see all leads we've converted into contacts and potentials. And when I click through from one of those Converted Leads the system presents the potential and contact that were created at the time of conversion. This information is also available as a report.

So, my questions are:

1) How can I get this information via the API? Specifically, how can I map the LEAD_ID to the CONTACT_ID?

2) How can I create a custom view (with columns of my choosing) that includes only "Converted Leads"?

3) How can I create a custom report filtering on "Converted Leads"?

Thanks,

Darrell