your GPU is too weak even for the native resolution, also the processor wouldn't get playable speeds on the Bleach series games. the menu and intro worked flawlessly since they are less demanding scenes.
you would preferably need a upgrade for better gameplay.
Sound stutters because it is synced to the fps. Slow fps = stuttering, slow, or just awful sound.
Maybe post screenshot of all of your pcsx2 settings. We might suggest you better settings. Though most likely the performance gain will be negligible.
Not a whole lot. Certain Athlons can be overclocked via FSB. But not all AM2 motherboards will allow that. Of course, this is at your own risk. Use the Nvidia proprietary driver. Use the latest git version as major improvements have been made. Ultimately, your hardware is quite old and can use a refresh.