In regards to your first question... there is no current way of doing what you are asking for.

However, I would like to mention that we can recommend you look at this way around, where you can run Test Sets suites called Build Verification Suites.
Even though, it might not apply for this scenario it is worth to mention it. Please note this functionality requires PC environment fully functional!

http://alm-help.saas.hpe.com/en/12.53/online_help/Content/UG/c_build_verification_overview.htm

The Build Verification module enables you to define a suite of automated functional test sets bundled together with a single performance test (called a build verification suite). When run together, the build verification suite checks the overall status of your build

In regards to question 2, when you add a test to a test set HPE QC/ALM actually creates a test instance ( seperate copy of the test ) and the tests in the Test Plan are design tests. Even thought they are the same test they are two different entities and have different tables in the database. There is no way from the GUI that you can see what Test Sets that a design tests has been aded to