Yes, it's definitely r^4. If we assume that the planet is far from the sun compared to the earth, such that the earth-planet distance and the sun-planet distance are both approximately r, then the amount of light the planet gets from the sun is proportional to 1/r^2. Then the planet reflects that light in all directions, and the fraction of it that comes back to us on earth is also proportional to 1/r^2. 1/r^2 * 1/r^2 = 1/r^4.

Yes. The solid angle subtended by the planet (and hence the amount of reflected light) goes as 1/r^2, and then the apparent brightness of the reflected light to us goes as an additional 1/r^2. The total dependence is then 1/r^2 * 1/r^2 = 1/r^4.

This is a really good physics puzzler.

The key point is that Pluto does not reflect light like a mirror, it scatters light relatively uniformly, causing more light loss to an observer than, say, a mirror that points the reflection directly at an Earth observer.

The light reaching the object from the sun drops off by 1/r^2, and then the light reaching Earth from the object drops again by 1/r^2. Since the latter light is a portion of the former, you multiply them for 1/r^4.