Type of Statistics in which the posterior probability is the updated belief on the probability of an event happening given the prior and the data observed.

Correct! The p-value is just the smallest significance level at which the null hypothesis would be rejected. But once you have chosen a significance level, e.g. 0.05, it would be incorrect to interpret p-values in reference to how close they are to your significance level.

Correct! Finding a p-value above the significance threshold (e.g. p-value > 0.05) means there is no evidence to reject your hypothesis, but not necessarily that the alternate hypothesis is true.