It is possible:
Go to Test Lab and select a test set which you want to move.
Click on Select Tests button present on top of grid view of test cases.
After clicking it, a pane at the right side of the window will get opened.
Collapse the hierarchy and go to the folder from which you want to get the test set.
Select that test set and Click on (<-) left ...
It is not possible to copy test cases from test lab to test plan. Actually test lab doesn't have any test cases, it only has a reference to test plan's test cases. So only way to copy test cases is from test plan to test plan.
For a functional requirement the Direct Cover Status depend on the test coverage for the same requirement.
In your example you have a functional requirement Req1 without test coverage and two requirement Scenario1 and Scenario2 with test coverage. The test coverage of Scenario1 and Scenario2 are not added to Req1 because they are not direct coverage tests.
Status of the requirement is automatically changed to Passed when all test cases from test set are passed, all test cases that cover the requirement are in this test set.
It's easy to do: when you add tests to the test set, select Requirements tree tab >> select the requirement >> press Add all tests that cover this requirement.
And do not forget that ...