What is the form of data used for prediction with generalized stacking ensemble?
Q1.  This can be done either way.  You may use only the base model predictions, or those and all the original features, or anywhere in between.  Passing along the original features may be known as "feature-weighted stacking," the idea being that the meta-estimator can learn that some of the base models are better on certain subsets of the original data (but AIUI the original approach there is to select/engineer more useful subsetting features, not to simply pass along all the original features; I assume this depends on context).

For example, the parameter passthrough in sklearn's StackingClassifier passes the original dataset along, as does use.feat in mlr's makeStackedLearner.

Q2.  Absolutely, making predictions requires each of the base models making their predictions (this can be done in parallel), then passing those off to the meta-estimator.

Q3.  Yes, a simple split suffices to prevent the data leak that occurs in more naive stacking, where the meta-estimator is fitted using the "predictions" of the base models on their own train set.  And yes, you will need another test set for evaluating the performance of the ensemble.  k-fold cross-validation is often recommended for the base models so that more data is available for all the models to train on.