The schema of the TestDirector database is documented in the Open Test Architecture Guide (Section 4, TestDirector Project Data Structure). All you need to be able to run your own queries is a login to the database server and a tool for running queries against the database for the project you are working on. If you want to query multiple projects, you need a login to every database that sits behind every project.
To find out what the databases are, you can use the Site Administrator interface of TestDirector.
What tools you need depends on the database you are using. Access using a pass-through query works for me.
When you are getting a login, it may be worth checking if you can get a read-only account so that you don't end up modifying something by mistake.
Depending on what you mean by a summary of pass/fail test cases, I'm not sure delving into the database is needed.
For summary metrics, the reports and graphs in Test Lab tab can be set up to report summary information and metrics without much trouble at all. These can be filtered for specific characteristics, grouped as desired, etc.
Even something like the "Current Test Set Report" gives you status and some of the detail. That can be exported to HTML or TXT for manipulation as needed.
Secondarily, the Document Generator tool gives good flexibility in generating such documents.
If you could be more specific about what you need for a summary, that might be helpful in coming to an easy solution.
The coverage report shows Pass/Fail test status for each requirement.
I'm not sure I understand the purpose of seeing the # test cases passed or failed for a particular requirement. If all test cases pass, the requirement is set to Passed. If one of them fails, the requirement is set to Failed.
Certainly, you can use OTA to extract the data you are looking for from the database directly, but make sure it's a good use of your time and gives you the value expected.