A power calculation determines whether the sample size in your experiment or study is big enough to give you a fair chance of proving your hypothesis if it is true. It is equivalent to a sample size calculation.
A "retrospective" power calculation is one that is carried out after the study has been run.
The Retrospective Power Calculator is a teaching aid. It is designed to help you understand why statisticians do not recommend retrospective power calculations. See the next item.
That's rather the point. See the previous item.
It's fair to say the method used is approximate. You'll notice that the output doesn't go to the trouble of defining "fully powered" or "underpowered" in any detail.
The answers it gives are usually right. If your answer to Question 1 is based on an incorrect analysis, or if you use assumptions that turn out to be wrong, then the power calculator will give you incorrect answers.
Click here for help with proper power calculations.
Click here for another retrospective power calculation.
Click here for help with significance tests.