After many trials and errors, I came to the conclusion that I am unable to fix this problem.
Trials and Errors
Almost everything used to work fine in the beginning. The only exception would be that my mesh's body would slightly deform while moving the right arm.
After many hours, I thought I had finally found the fix by removing some faces inside the model. That fixed the deforming problem but made it so that the right hand would be the only thing to gain weight when doing automatic weights.
After manually changing the weight to 0 the hand wouldn't move at all. I tried making a new arm with new bones, but that still didn't fix the problem.
I then removed half of my model and mirrored it again, symmetrized the bones and now some vertices don't move even though that arm moves perfectly fine.
Here's my .blend file: