Can the philosophical mysteries be solved at all?
None of those are unanswerable. The question of whether god exists is answered, its just people who believe in god and certain types of fence sitters still carry on regardless, attached for whatever reason to the indefensible believer position.
Free will is a bit trickier I’ll grant you but I feel like its mostly a problem of definition of free will. If its defined as something outside deterministic forces, cause and effect but if the definition isnt magical and accounts for deterministic forces then sure, free will exists. As Hitchens used to say, we have free will becuase we have no choice
Lastly, life after death. Like god, this has been asked and answered. No, we have no good reasons to think there is life after death.
There is certainly things beyond human understanding, but none of the things you mentioned are. All understandable, all have fairly clear answers. Whether or not those answers can overcome indoctrinated belief or strong emotional bias is another matter.