The C# version may be slow due to the IKVM translation. We need to look into it before giving a definite answer.
This is simple. For a k-step-ahead prediction, we just need to do it one step at a time. E.g., see pages 51 – 52 of this tutorial: http://jhqian.org/ec310/06timeseries.pdf
(You basically plug the residual values and past vol forecasts into the GARCH model iteratively for k steps.)
I am not exactly sure what you are asking. You seem to have already answered your own questions. Basically, GARCH predicts the variance of the residuals (hence the variance of the conditional mean/forecast); ARMA predicts the conditional mean (which you use for your forecast).