Can the philosophical mysteries be solved at all?
I think that it is not simply a matter of whether we can solve the mysteries, but to what extent? I think that it is inevitable that we wonder about the existence of God, and whether there is life after death and, probably most human beings have asked the questions. It could be that some people just grow up in a secular context and don't see the relevance, of course.
Generally, I believe that the metaphysical questions of philosophy are about finding explanations and giving us a framework to for finding meaning, and that both aspects are important. Some reductionist philosophies may provide explanations but don't give any basis for mythic structures. Of course, it may be that people can create their own, but that can be difficult. In contrast, some religious or mystic philosophies can be seen as more romantic, and inadequate for providing causal explanations. So, it is an art of juggling this to come up with systems of thinking which work for us individually.
As you can imagine from my various threads and posts, I dwell on these matters a lot, whereas many don't agonise in quite the way which I do. But, I most certainly would not give up exploring or suggest that anyone should not bother trying to look at the questions, just because they are difficult. I would go as far as to say that it is this searching which is central to my own values, and if I stopped thinking about such issues, I would probably not have a reason to get out of bed each day.
I don't know if my answer is of any help to you, but, personally, I wouldn't give it up? What are you going to replace it with?