We present the results from Atacama Large Millimeter/submillimeter Array imaging in the [N II] 205 mu m fine-structure line (hereafter [N II]) and the underlying continuum of BRI 1202-0725, an interacting galaxy system at z = 4.7, consisting of a quasi-stellar object (QSO), a submillimeter galaxy (SMG), and two Ly alpha emitters, all within similar to 25 kpc of the QSO. We detect the QSO and SMG in both [N II] and continuum. At the similar to 1 '' (or 6.6 kpc) resolution, both the QSO and SMG are resolved in [N II], with the de-convolved major axes of similar to 9 and similar to 14 kpc, respectively. In contrast, their continuum emissions are much more compact and unresolved even at an enhanced resolution of similar to 0 ''.7. The ratio of the [N II] flux to the existing CO(7-6) flux is used to constrain the dust temperature (T-dust) for a more accurate determination of the FIR luminosity L-FIR. Our best estimated T-dust equals 43 (+/- 2) K for both galaxies (assuming an emissivity index beta = 1.8). The resulting LCO(7-6)/LFIR ratios are statistically consistent with that of local luminous infrared galaxies, confirming that LCO(7-6) traces the star formation (SF) rate (SFR) in these galaxies. We estimate that the ongoing SF of the QSO (SMG) has an SFR of 5.1 (6.9) x 10(3) M-circle dot yr(-1) (+/- 30%) assuming Chabrier initial mass function, takes place within a diameter (at half maximum) of 1.3 (1.5) kpc, and will consume the existing 5 (5) x 10(11) M-circle dot of molecular gas in 10 (7) x 10(7) years.