The shell would immediately collapse into a smaller solid body. On the scale of an earth-sized planet, rock has all the structural integrity of silly putty. The shell's self-gravitation would tear it to pieces and pull those pieces in toward the center of mass. You'd end up with jumbled fragments of the crust forming a new, much smaller planet. It might look a lot like Uranus's moon Miranda.

 

Assuming some sort of magic maintained the shell as a solid, the gravity would be reduced proportional to the fraction of the planet's mass that had been removed. One of the most useful results from Newtonian physics is that, outside of a sphere of matter with a radially symmetric mass distribution, the math works out that you can calculate gravity as if all the mass were concentrated at the center of the sphere. (Even more fun, if you move into such a sphere (e.g. down a vertical shaft), you can just ignore the part of the sphere with a greater radius than yours. Which means that gravity is precisely zero everywhere inside a hollow radially-uniform spherical shell.)

 

Yep. The surface is just a special case of "outside the sphere" above. The gravitational pull at any distance would be reduced proportional to the decrease in total mass.

 

For a Sol-type system, not appreciably. You'd see changes in the future orbits of the other worlds, but it would take centuries for them to become significant, and even then, everything would very likely remain stable. 

However, if the world had moons, they have almost certainly been lost. The most likely scenario is that they are now orbiting the parent star as independent dwarf planets, all on orbits similar to that of the planet itself. This is a hideously dangerous situation; over the course of time, odds are rather high that one or more of the moons will impact the planet.