Hi Michele,
Your interpretation of both points is correct. My idea was that of giving you two options:
a) use the prior described in ex 2.1
b) use the posterior estimate from ex. 1 as a prior for ex. 2.2
In the first case, you would ideally get a similar result from both exercises.
In the second case you would get a "refinement" of your first estimate and ex 2.2 would also be a double check for both exercises. In fact, if the analysis of convergence and the implementation of Gibbs sampler are correct, the posterior estimate of ex.2.2 should not change much wrt the prior, as you pointed out.
Best
Ginevra