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I am having issues understanding the J test, where J=mF. Can you please explain the solutions to Question 5, parts (e) and (f)?

For part (e) I understand we reject the null because we find X12 from the equation X2m-k. Where M is the number of instruments and K is the number of regressos. But I do not understand how to tell the difference between regressors and instruments. Which 2 variables are instruments are which variable is the regressor?

For part (f) I do not understand why we used 6.63 to test. My table says this is the .01 significant test for 1 degree of freedom, but the stata output says 2 degrees of freedom?

Here is the question, with the handwritten solutions at the end