How to measure uncertainty and prediction errors for a naive Bayesian Classifier?
You can check the probability returned by your model. Just be aware that probability is not uncertainty but if you calibrate your probabilities, you can have an idea of the belief of event realisation from a frequentist point of view.

For the error of prediction, with a calibrated classifier if you have a probability of 0.8 to belong to a certain class, you can expect that there is a 80% chance that your sample actually belongs to this class.