From what I understand: all points in space are being pushed away from each other; from two atoms in your hand to two atoms across the universe. The reason objects aren't getting bigger is because atomic/nuclear/gravitational forces hold nearby objects together: if you stretched the earth to be a millimeter wider (massive amount), the earth would just collapse down to the same size it was before. Objects are held together locally, but pushed apart globally.
Not quite, expansion doesn't happen on such small scales.
Expansion is a property of the Friedman-Lemaitre-Robertson-Walker metric, which is a solution to the Einstein equations if you assume everything is isotropic and homogeneous. Spacetime around a star or a galaxy is obviously not homogeneous. It looks much more like a Schwarzschild metric, which features no expansion.
It may help to think of the universe as a cake with raisins in it. When you bake the cake, the dough expands uniformly, but the raisins do not.
Small caveat: If dark energy has a certain property, it changes things and a "big rip" will occur, tearing apart everything but elementary particles.
from my understanding, it happens at ever scale. But the other forces (weak, strong, gravity, electromagnetism) are MUCH more powerful than that at small scales, and thus not observable at small scales.
Don't take my word for it, but I think of it as magnets on a stretchy scarf. Three magnets that are already clumped together stay together but other clumps become further and further removed.
