If I'm understanding your question correctly, you're basically asking how to view your automated (i.e., UFT created) scripts in QC and run them (along with Requirement/Defect traceability/coverage).

In order to see your recorded test steps (i.e., the script), make sure you have the UFT ALM Plugin installed. This is included during the normal UFT installation. Log into QC, go to Test Plan and select an automated test (e.g., the one you just created in UFT and saved to QC). Note in Details the Test Type shows QUICKTEST_TEST (as opposed to MANUAL, etc.). Click on the Test Script tab (between Design Steps and Parameters). If the UFT ALM Plugin is installed, your script will display. If it doesn't (and complains about the Plugin/Add-in not being installed), open Windows Control Panel > Select 'HP Unified Functional Testing' > Change > Next > Change > Make sure 'ALM Plugin' Will be installed on local hard drive > Next > Change.

From here, your automated test will behave like any other test (where you can go to the Req Coverage tab to link requirements, Linked Defects tab to see linked Defects, etc.).

To run your tests, go to QC Test Lab, create a Test Set, and click Select Tests add your automated test(s). Click the Run button, and it will open Automatic Runner. If you're on the same machine with UFT, you can choose to Run All Tests Locally and run your tests (which will open UFT to run through the script(s)). The results of the tests will be captured, and again, it will behave like any other manual test with whatever coverage you've specified.

Note: Sprinter is for manual tests, so you will not use it to run your UFT automated tests.