# 4. 
Yes, why not? The concept is simple: you have a candidate variable that may be helpful in predicting some other variable (even after accounting for a bunch of other predictors such as own past values of the dependent variable). You test whether that is the case. If you reject the null, you conclude that the variable indeed helps.

# 5. 
Because the two partly overlap. The difference is that the Granger test is used in a VAR model where there is more than one dependent variable and hence more room for applying the test (Does $y_1 \xrightarrow{Granger} y_2$?; Does $y_1 \xrightarrow{Granger} y_3$?; etc). Meanwhile, Choi and Varian has only one dependent variable.

> Granger can measure the direction of the effect

You can test $H_0 \colon y_1 \xrightarrow{Granger} y_2$ and $H_0 \colon y_2 \xrightarrow{Granger} y_1$ and conclude which way (none, first, second or both) it goes. So in this sense you are right.

> Choi & Varian's model can help to measure the magnitude of the effect

Yes. But also a VAR model allows measuring the magnitude of effects alongside Granger testing; hence, Choi and Varian are not superior in this sense.

> Granger can measure the direction of the effect while Choi & Varian's model can help to measure the magnitude of the effect

As becomes clear from above, magnitude can be measured in both cases. Direction may or may not be of interest. If it is, do Granger tests. If it is not, a single Choi and Varian-style test is enough.