1. how to write variance equation in GARCH when using EVIEW? (I have tried, but there always appears ".....not defined") ?

try it again! try every thing you have seen in the panel /window, it is not hard at all. Or you can first read the user's guide for Eviews for this particular chapter. It takes , say 1-2 hours

2. how to set the intercept equal to zero in the variance equation in GARCH when using EVIEW? (I want to estimate lamada in RiskMetrics approach which is a special version of AR and GARCH )

Asymptotically, use the t-statistic for Omega, it is of a normal one

3. Under which circumstance, the intercept of the mean equation and variance equation should be set to be equal to zero? (I use long-time horizon data and find the estimated intercept parameter is very small. Can I set it to be zero? ) You can use AIC or BIC to determine the AR order in the mean eqn.(at this stage you can ignore conditional variance part). or you can do maximumlikelihood for this whole system(mean and vairance eqns)

if model exchange rate or stock index return. if you want to be lazy, demean them and ignore the intercept(constant=0). It is also safe to do so by the Market efficiency hypothesis