Clearly all the overlapping points in the first graph are obscuring most of what's going on. This is a warning flag that the author may be trying color the facts to suit their argument.
Not very clear what you are try to say:
(1) What "standard deviation"? Perhaps you mean the standard error of the correlation coefficient is large relative to the its estimated value. Given the large number of data points it is likely to be quite small. Another warning flag is the failure to report either the correlation coefficient or its standard error.
(2) What does "ellipse isn't irregular" mean? Given all the overlapping data points the shape of the plot is entirely driven outliers. To my eye this looks what you would get from plotting a bivariate normal distribution.
(3) Kepler? The linked graph? How is this helpful in understanding what's going on?
The first graph has a straightforward interpretation: you are making two imperfect measurements of each teacher's performance at two different times. There is noise in both measurements and teacher performance may have actually changed between measurements.