How can I run the Japanese version or the other regions of the game off the disc?
You would need to region unlock your Wii through hacking. The SRA page has a section dedicated to videos that have helped me in doing this years ago. You need the region's disc to actually be able to play on that version. JP is no different from the US version in case you were wondering, but if its the only disc you have then this page will help. https://beta.speedrunacademy.com/games/ssbb/guides/brawl-speedrun-setup
I keep getting an unable to read disc error. How do I fix that?
Did you follow the linked page's video tutorials? Installed Homebrew and Priiloader? If you did then the disc could have too many scratches that could make it unreadable.
You could look at the comments about boot2, I personally don't know since I installed everything without issues from these videos.