I'm just curious about that the existence of non-rotating stars. Is it physically possible for a star not to rotate at all? Does magnetic braking eventually stop the stellar rotation?
No, this is not possible.
During the stellar formation, some angular momentum will always be present. And any "braking" effects (magnetic, relativistic, tidal etc.) will become weaker as the rotation slows down. So the rotation will never completely stop, because any forces slowing down the rotation will weaken as well.