Welcome!
- That is correct.
- Better is a highly context-specific thing. But whether you model the “inputs” is typically more of a modeling decision than a decision about how to conduct a prior predictive check (i.e., sometimes you just want to take your predictors as given and not model the generative process by which they come about and other times, you do). That being said, you would ultimately need to figure out if you wanted your prior predictive to inform the question “do my priors match my intuition about my model and my observed input/predictor values?” (in which case you should just use your observed inputs/predictors) or the question “do my priors match my intuition about my model and plausible input/predictor values?” (in which case you may choose to figure out what plausible values look like, generate some, and then conduct your prior predictive check).