MIDAS is useful when you have a low frequency series and you want to include high frequency data in the regression. So for instance, if you want to forecast quarterly GDP data and want to include daily S&P 500 data as a regressor instead of just using the quarter end value of S&P 500.
Usually we assume that the causality runs from S&P 500 to GDP. It becomes trickier when you start thinking about the impact of lagged GDP on S&P 500. You can usually get away with some kind of ad hoc adjustment like filling in the GDP growth rate for each daily period as equal to the quarterly growth rate, but it won't necessarily capture the relationship properly.
State space methods, such as Kalman Filters, are another common approach to handling mixed data series. The Philly Fed's ADS business conditions index and the literature on Nowcasting use this. It's a large, complicated literature that is probably beyond a small post to summarize. To get a general sense of the approach, they assume that the data is missing and then use Kalman Filters to estimate parameters given the missing data.
Another approach is to use a combination of forecasting models. In the above S&P 500 and GDP example, you could use a daily forecasting model that includes GDP and a quarterly forecasting model that includes it. You can use the daily model to forecast iteratively out for the remainder of the quarter and then use the quarterly model thereafter. This approach could be made significantly richer with monthly models, etc.
With respect to your second question, the hard part is estimating the model. Once you have the model set up and estimate the parameters of it, forecasting is usually straightforward.