1) The RE flag is the tricolour with the Savoy emblem in the middle of the white isn't it ?
2) The EI one is the plain tricolour ?
Answer: yes again, but E.I. (Esercito Italiano) is post-WW2
3) The Partisans' ones : with or without the Royal emblem according to their obediance ?
Answer: yes, more or less, but it also depended on circumstances (availability of the "right" flag).