Yes yes yes yes yes yes yes yes
Force can be exerted into an object with out it moving, but if you were to move the object due to force it would be considered work. (yes, you can exert force without having the object moving)
Answer: 
Explanation:
The equation to calculate the center of mass
of a particle system is:

In this case we can arrange for one dimension, assuming the geometric center of the Earth and the ladder are on a line, and assuming original center of mass located at the Earth's geometric center:

Where:
is the mass of the Earth
is the mass of 1 billion people
is the radius of the Earth
is the distance between the center of the Earth and the position of the people (2 m above the Earth's surface)

This is the displacement of Earth's center of mass from the original center.
It will be a little bit less because of evaporation i learned that in third grade and your in high school that is sad