I am not sure if I understood everything correctly
I tested your save.
Health regeneration perk works without problems. No matter whether with or without an opponent when using your two-handed weapon.
Combat music is supposed to be a warning. If you have an opponent who is well below your level (50!), it will not sound because it is not a challenge for you.
Food only works outside of combat mode.
So I think everything works correctly for you as intended.