I understand that “The Out of Bounds” is banned from Any% No OoB. Are any other glitches allowed in this category or is it completely glitchless?

Pretty much all the other glitches are allowed in this category, except for Crown Theft, which is banned from all the categories as it doesn't play the credits. Other than that, one cycles, R-pumping, and text skips are all things that are allowed!

crown theft isn't banned, it's just a softlock

Any differences in NSO Gamecube?

Mostly in loads as far as I'm aware, plus the lack of laggy rooms. I believe the JP version has most if not all JP exclusive glitches patched so it's essentially like the NTSC-U version on emulator with Japanese text.