Quality is delighting customers
What do you mean by moving? rather why do you want them to move up/down?
Yes, we can move the testcases up/down in Test Lab
Test plans in test lab!! are you sure you are asking the correct question? A test set consists of test scripts. And there is an option of ordering tests under the execution flow tab. Check it out.
I believe QC does not have any way to update test results of multiple test cases all at once. The fastest way to update multiple tests is the following :-
1. Just update one test as passed (Make sure you are in grid view).
2. Now click on that "passed" cell and it should get highlighted. Now just keep repeating the remaining steps.
3. copy (cntr +c) duh.
4. now hit down arrow to go to the next test.