Hello thinkandmull. I am currently studying for a PhD in particle theory, so I think I can help you out.
A lot of people have the idea that QM is a magical idea that makes nature unknowable. That technically isn’t true; at the fundamental level, QM is a very thinly disguised theory of linear algebra. Particles have wave-like properties, but fundamentally, they are governed by algebraic properties that restrict their structure to a few configurations, known as eigenfunctions. The uncertainty between position and momentum certainly exists, but they are simply the result of the inability of the position and momentum matrices to be simultaneously diagonalized. What this means is that certain values of these particles cannot be measured with 100% certainty at the same time, but we can know how these particles act on a macroscopic scale.
As for your point about particles appearing and disappearing at will, this is a facet of the theory of quantum fields, or QFT. QFT is quite a bit more complicated than quantum mechanics, so I won’t go into it here; basically, the particles that disappear and reappear are called “virtual” particles, and aren’t really what we consider particles at all. They are merely (in some interpretations) mathematical crutches that arise from the difficulty in solving the equations of motion of particles in this quantum field. Think of them like ripples in the quantum field. However, their behavior is well understood and there is nothing unknown about why they are there.
I’m glad you are thinking about the philosophical implications of QM (many physicists don’t even want to think about them

) But there is no conflict between QM and Catholic spirituality. Relics may be filled with virtual particles which have fundamental uncertainty, but the essence of the Relics is there all the same