No, that's not right. The presence of the Earth has no effect on the force between you & your marble. The force is much smaller than the force between the Earth & the marble, but that's not the point. The OP is right, there is a force between him & his marble, and the Cavendish experiment is a clever way of measuring it.
Difficult but not impossible. In general, that's pretty close to what Cavendish did.
The Cavendish experiment is routinely done in physics classes. It is done by measuring the attraction between two sets of weights, one set is large and the other is small. No mountains are involved. The weights are arranged in a torsional balance, what gets measured is the 'twist' induced by the gravitational force (and counteracted by the torsion of the twisting wire). Check google or wiki for a more detailed explanation with some graphics to make the setup more clear.
As far as the mountain goes, Cavendish used the result to calculate the mass & density of the earth. Maybe that's what you're trying to remember.