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Your first question is answered by quantum theory. The "orbits" of the electron in Hydrogen are quantized. The only way an electron can change its energy is by jumping between levels and emitting light. Once the electron sits in the ground state of atom, the lowest energy state, it can't go down anymore because of quantum effects. For more complicated atoms, all the discrete states up to a certain energy are filled, and the atom is stable because of the Pauli exclusion principle which tells you that no two electrons can be in the same quantum state.
To answer your second question, remember that as you compress the atom you are applying an additional force, but the force from the nucleus also gets stronger as the electron moves further in. The system will find a new equilibrium and the electron will not collapse into the nucleus in general. In practice, you could alter the orbit with electric and magnetic fields, but the electron isn't going to crash into the nucleus.