Regarding question 1: my understanding is that using find_MAP is not recommended. I remember reading Thomas Wiecki saying that find_MAP is only there for historical reasons. You do prediction with sample_ppc (or sample_posterior_predictive in the future). If you need the expected value of the prediction, take a mean of your generated samples. If you need to look at the variance/uncertainty of the prediction, take the variance or take quantiles from your samples, etc. This relates to your question 2.
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