OK, here are a few things that struck me as odd:
Immunity is 8 refresh and it is better than Mythic Toughness and Mythic Recovery together, which are 12 refresh. Why?
Because either alone is almost as good as Physical Immunity, but not quite? And they also grant ancilliary benefits, like going without sleep or other rest indefinirtely (something Physical Immunity most certainly does not).
Living Dead, which prevents death, is not labelled as a toughness power. Does this mean that things that affect toughness powers (such as Soulfire and "All creatures are equal before God") do not apply to it?
No idea as a general rule, though "All Creatures Are Equal Before God" would seem to trump it quite thoroughly thematically speaking.
Living Dead mentions that supernatural help is required to recover from physical consequences but it also mentions you can't recover on you own. Does having recovery powers (which are supernatural) help with recovery or not?
I'd rule yes, they do. But there's no definitive answer as it was really not intended for PC use.
There are almost no toughness abilities that apply to mental attacks whatsoever. A still-green wizard usually is almost as resilient mentally as a Denarian because there are no abilities that reflect a supernaturally strong mind, mental protection or similar. Why?
Which is as it should be. Look how quickly Quintus Cassius crumbled in Death Masks. Age and power do not inherently grant mental fortitude in and of themselves. Nor should they. Inhuman creatures in the Dresden Files may know more or be more powerful than humans, but they are not inherently stronger willed.
