Regarding #1, you should keep it in Cartesian.
Regarding #1, it actually does not matter much whether you use Cartesian or Fractional because you are supposed to do ion relaxation after applying macroscopic strain to the cell, i.e.,it means that you change cell shape and/or volume. But I would suggest keeping the coordinates in Fractional because in some cases, e.g., when pure hydrostatic stress is applied, the symmetry of the lattice does not change, and the atoms keep their positions (given n Fractional coordinates) with respect to the new lattice vectors of the strained cell. In fact, even if there is only some hydrostatic contribution to the total strain, it would be beneficial to keep the coordinates in Fractional, since the new atomic position will then be closer to the equilibrium ones in the new (strained) lattice.
