I have looked through a bunch of resources, but I can't find a comprehensive account which would answer my question(s).
I understand PA is consistent assuming that Primitive Recursive Arithmetic is consistent and that the ordinal $\epsilon_0$ exists. But here's where things get confusing, I can't seem to find a coherent account from this point downwards. Wikipedia seems to list the proof-theoretic ordinal of PRA here as $\omega^\omega$, but I can't seem to find what is the underlying theory for the consistency proof of PRA, similarly to the way PRA acts as base for PA. Moreover nowhere do I seem to find a statement if such a tower of ordinals and base theories is finite or infinite. I would assume it's finite from the way the Gentzen's consistency proof is normally presented, as being relatively finitistic. How does this tower look like, where's the bottom of the ordinal analysis leading to Gentzen's consistency proof?
Another related point is that some articles seem to imply that proof-theoretic ordinals don't make much sense for Robinson's Q. Is there a weakest undecidable theory for which ordinal analysis starts making sense?