You generally want your assessment set (as well as the test set) to have the same distributions as data that you would see "in the wild". I would not sample those data within resampling.
Yes to that. This is how resampling estimates the variation in your modeling process. There will most likely be different results within resamples.
During resample, the recipe should be executed (=trained) on every analysis set separately. Within each fold, it is applied to each analysis and assessment set.
Outside of resampling, once you've settled on a final series of steps, the recipe is applied to the entire training set and applied (=baked) to the training set (that will be used to build your final model) and for any other data set where predictions are needed.