If the time series has autocorrelation then you are right then square root of time scaling is not applicable. Normally autocorrelation is removed using GARCH framework or ARMA/GARCH framework then you get heteroskedastic volatility by definition of GARCH.
For the second part of the question, say, you are looking at Black-scholes model. For that the volatility is assumed to be constant and is the volatility at maturity. So, volatility used is the forecasted volatility at maturity. You can forecast that volatility using GARCH also, for the sake of fitting into the BS formula.