I am guessing you run OptimizeGeometry with various pressures. You can then uase the initial_state argument to the ATK calculator to start one calculation from the self-consistent ground state from another calculation.
1+2: Yes, if you start the calculation at 20 GPa from the configuration obtained at 10 GPA, without changing the calculator, you should obtain the same result, and often (but not always) in fewer SCF iterations.
3: Yes, but bear in mind that this works best if you do not make drastic changes to the configuration (like changing elements) or to the calculator (like changing k-point sampling).