- You will need to either (1) omit variables for which you cannot provide future values, (2) forecast them separately, or (3) provide scenario values for them. See https://otexts.com/fpp3/forecasting-regression.html. Using a mean or median of the historical data is one possible way of forecasting them, but it may not be the best.
- Minimize the AIC is best. PCA can also be effective but does not guarantee you the best predictive variables.