In ATS you can create folders and within folders you can add test cases and test suites. You can compare the folders with the folders you can create in Documents on your PC. In the same way you can create a structure in ATS. Test suites contain a reference to test cases and or other test suites that are intended to be used to test your app to show that it has some specified set of behaviors. So by collecting specific test cases in a test suite you can also organize/manage your test cases.
You cannot reduce the execution time of a test case in ATS. The execution time of test cases is usually "as fast as possible". The execution time is dependent on the communication between ATS and the chosen selenium host and between the selenium host and the application, because a connection needs to be made. The timing during recording does not affect the execution time.
You could speed up test execution by running test suites in parallel. But to be able to do this you your selenium hub needs to support parallel sessions. If it does ATS will automatically select multiple nodes when running test cases. In a test suite you can select yourself whether you want to run the items in the test suite in parallel or sequential. Please be aware that being able to run test cases is parallel also depends on the right of your app. If a user can only log in once then running tests in parallel on that same user would result in failed test cases.
Please let me know if anything is unclear 😊