The answer is: it is perfectly all right to use SQL*Plus, Toad, SQL Developer, PL/SQL Developer, etc. to write and execute code to help you answer the quiz.
You should not (and, in fact, you should not be able to) copy and paste code from a quiz, and then simply execute it. But as I note, you should not be able to do this; most quizzes present code as an image. If the code is accessible for copying, then it is not (or, shall I say, should not be) a competitive quiz (rankings and prizes) and we don't really care if you copy and paste.
But if you want to take the time to type in a block of code (or more), then execute that code to see the results, please go right ahead. The most important objective of the PL/SQL Challenge is to improve your knowledge of PL/SQL (and SQL and APEX and....). I can think of few better ways to do this then to write code.
You will, of course, be "penalized" for taking the time to write code; your score will be reduced by the extra time required to do so. But it is definitely not cheating.