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In EV7, the "Estimation weighting matrix" and "Standard errors & covariance computation" can now be separated (In EV5, only allow in panel equations objects). What are the advantages?
some textbooks say that the optimal one is W=C^(-1) where W is the gmm weighting and C is the covariance matrix. Under what situations should different methods be used for the estimation of W and C?

In finite iteration GMM estimation there is a question over which residuals you should use in the computation of the covariance matrix. Should it be those that were used during the computation of the estimation weighting matrix (i.e. residuals calculated using the previous iteration's coefficients) (Estimation default), or should you calculate a new set of residuals using the final estimation coefficients (Estimation updated). There is no right or wrong answer to this, hence why we offer both. I imagine that the vast majority of users will want to use one of those two options.

As to why you might want a different functional form for the covariance matrix, well once obvious case is if you've used a TSLS type weighting matrix for estimation, but then want to adjust the standard errors for heteroskedasticity or autocorrelation.

I can think of no good reason why you might want to estimate using a HAC weighting matrix and then impose a White structure on the covariance matrix, but the option is there just for the sake of completeness.

I'm not sure what Gareth mean. If I estimate the weighting matrix by HAC to adjust the hetero and autocorrelation problem, then use the HAC to estimate the covariance matrix is still meaningful? I mean that, when I estimate the wieghting matirx, the hetero and autocorrelation problem should have been corrected. In this situation, should I estimate the covariance matrix by HAC or by EViews default?