The red point appear when you refresh the graph. They are the points (diamonds) you’ve already clicked on that show up in the history list below the plot.
For the cut estimator, the data comes from the grading report. For GIA reports, there’s a proportions diagram. In the sample grading report below, the table % is 58%, the crown angle is 35.5, and the pavilion angle is 41. If it’s from another grading lab, those numbers are either listed directly or are also shown in a similar diagram.