When the residuals appear to be heteroscedasticity, then can we say the error terms are correlated with the independent variables ?

For me, i dont think we can say anything in terms of the correlation between indepeandent variables and the error terms, but one thing for sure is that the standard error of the estimated coefficients would be biased and estimated parameters are not bias.

Unconditional Heteroschedasticity is usually not a problem.

Conditional H. and ARCH need to be corrected.

You can test for Conditional H using BP Chi Squared Test.

You can test for ARCH by regressing errors on their t-1 lagged values. If the slope term is statistically significant, you have ARCH (it means the squared error depends on its previous period value).

ARCH does have the benefit of allowing us to forecast variance at t+1.