Hi Francesco,
keep in mind that this exercise does not admit a unique possible solution and that my answer refers to the generative process I thought about when building the exercise. You may come up with a different plausible answer.
1) You could simply use the same distribution for all the z_t, in such a way that z_1 only depends on theta, while the others also depend on z_{t-1}.
2) You're right, the z_t are not independent, so you are not supposed to use pyro.plate on them. In fact, if you look at the original graph, only theta and mu vectors are represented in plate notation. You can use both a for loop or sequential sampling calls, since there are only three variables in this case.
Ginevra