Beta is the type II error. It's the probability of not rejecting H0 when H0 is false.
To calculate beta, first you need to get the rejection/acceptance region based on your H0, H1 and significance level, then you can get the conditional probability of the acceptance region given H0 is false.
You have alpha=.05, critical value of 1.645 is correct. Calculate the standard error of the mean, then the critical value is the z-value for the boundary of the rejection region. Rejection region should be Xbar>...
Very good question. When you try to find the rejection region, you use the mu in your H0. After you get the region, you use mu=56, notice I've always included the condition mu=56 afterwards. This is a KEY concept in power calculation.