1 The charge distribution on the inner surface does not affect the charge distribution on the outer surface, because the inside of the metal is shielded by the metal, and the outside of the metal does not affect the inside, and vice versa, that is, the metal shields the influence of the inside of the metal on the outside. However, due to the conservation of charges, the sum of internal and external surface charges remains unchanged.

There is a popular understanding that if there is an electric field distribution in the metal, this electric field will promote the movement of electrons in the metal, and the movement of electrons will produce a reverse electric field, which will eventually completely offset the hypothetical electric field (for example, the water surface is uneven, but it will eventually become horizontal through the free flow of water), so there is no electric field in the metal. So the electric field outside the metal cavity can only stop on the metal surface. No matter how the external electric field lines dance, once they touch metal, they will be cut off. In more detail, the electrons on the metal surface will interact with the external electric field, making the combined field strength of the metal surface perpendicular to the surface (as long as it is not vertical, the surface electrons will be affected by the horizontal field strength, thus moving until the combined field strength is vertical). Therefore, because the field strength is broken on the outer surface, the metal inside does not know the change outside, that is, it is shielded. On the other hand, I think the same thing both internally and externally.

If it is grounded, the outer surface will be forced to zero, and even the ability of the inner surface to influence the amount of charge on the outer surface will be eliminated.

4 is very close, similar to the neighborhood in mathematics.