Yes, you should use granger test of lag=12. your second question -I am assuming that you have chosen lag 12 because Godfrey LM test suggested it was okay, Please ensure that there is no residual autocorrelated residuals before doing anything, You can increase your lag, add seasonal dummies, impulse dummies for AFC and GFC to solve auto first before proceeding. Granger test cannot be valid in the presence of serial correlation.

But, before estimating VAR model, test the degree of integration of each variable and then test the presence of cointegration and decide to estimate either VAR in first diffreences or VECM. Finally you can implement granger causality based on your model!

If your aim is to test for Granger causality there is an issue of whether the data are stationary or nonstationary and whether a VAR in differences, levels or a VECM in differences and levels should be used. This requires cointegration testing. If the data are stationary you can use the VAR in levels. If the data are nonstationary and not cointegrated you need a VAR with differenced variables, however, if the data are cointegrated you need a VECM in differences and levels. A way around the Granger-causality testing in a VECM (that has short-run and long-run components) is to use the Toda and Yamamoto (1995) surplus lag Granger-causality test. See Dave Giles blog for a discussion of this - the link is given below.

https://davegiles.blogspot.com/2011/04/testing-for-granger-causality.html?showComment=1320248137553#c4210543007105661619

If your aim is to forecast you might want to use information criteria (such as AIC and Schwarz) to determine an initial lag length and then test for autocorrelation. You would probably want the shortest VAR lag length (for efficiency) that avoids evident autocorrelation.

It is difficult to advise on forecasting without a good understanding of the variables being forecast. The remarks below are made in a general context without any such understanding.

1. A key feature of any forecast is that the forecast error in unpredictable. if you have autocorrelation in your forecast error it can beforecast given past values. then your forecast is not optimum and can be improved.

2. The evaluation of alternative forecasts uses a particular methodology. Measures of within sample do not work. Such methods often lead to overfitting and bad forecasts. If you can find a copy this is well covered in Granger and Newbold (1986), Forecasting economic time series. A more modern approach is Diebold, Francis X - Forecasting in Economics, Business, Finance and Beyond - Edition 2017 which can be downloaded from https://www.sas.upenn.edu/~fdiebold/Textbooks.html Basically one takes the initial part of the sample, estimates the forecasting model, calculates forecast(s) at required horizons and derives forecast errors at these horizon(s). Now advance the estimation sample one observation and repeat the process. You then end up with a series of out of estimation sample forecast errors. An examination of these out of sample forecast errors which can be used to evaluate and compare different sampling models. (Your software should be capable of doing the calculations required.

3. A VAR, with lag length 12 is almost certain to overfit your data which will lead to poor forecasts. A 3-variable VAR with 12 lags and a constant requires the estimation of 111 coefficients and 9 variances/covariances. This difficulty can be overcome by the use of Bayesian VARS (e.g. Minesota Prior). (Software Rats - Estima.com, R, Matlab (?) and possible others) (Chapter 9 of Elliott & Timmermann (2016), Princeton - graduate/reference text on forecasting)

4. I would not recommend the use of bivariate Granger causality tests. Say your main interest is variable X. Say variable Y Granger causes variable j at lag 1. Say Variable Z Granger causes variable Y at lag 1 but does not Granger cause variable X in a bivariate VAR with X and Z. You will however find that variable Z does Granger Cause variable X in a 3 variable test. What you are suggesting is similar to deciding what variables to include in an OLS be looking at bivariate correlations between the dependent variable and candidate explanatory variables.

5. You might find some of the articles in Clements and Hendry (2002) A companion to economic forecasting, Blackwell of use. There are several articles in that compilation thea contain comparisons of different forecasting models.