We present the results from our Atacama Large Millimeter/submillimeter Array (ALMA) imaging observations of the CO (7-6), [CI] 370 um (hereafter [CI]) and [NII] 205 um (hereafter [NI]I) lines and their underlying continuum emission of BRI 1335-0417, an infrared bright quasar at z = 4.407. At the achieved resolutions of 1.1 to 1.2 (or 7.5 to 8.2 kpc), the continuum at 205 and 372 um (rest-frame), the CO (7-6), and the [CI] emissions are at best barely resolved whereas the [NII] emission is well resolved with an ALMA beam de-convolved major axis of 1.3 (+/- 0.3) or 9 (+/-2) kpc. As a warm dense gas tracer, the CO (7-6) emission shows a more compact spatial distribution and a significantly higher peak velocity dispersion than the other two lines that probe lower density gas, a picture favoring a merger-triggered star formation (SF) scenario over an orderly rotating SF disk. The CO (7-6) data also indicate a possible QSO-driven gas outflow that reaches a maximum line-of-sight velocity of 500 to 600 km/s. The far-infrared (FIR) dust temperature (T_dust) of 41.5 K from a gray-body fit to the continuum agrees well with the average T_dust inferred from various line luminosity ratios. The resulting L_CO(7-6)/L_FIR luminosity ratio is consistent with that of local luminous infrared galaxies powered predominantly by SF. The CO(7-6) luminosity-inferred SF rate is 5.1 (+/-1.5) x 10^3 M_solar/yr . The system has an effective star-forming region of 1.7 (+1.7/-0.8) kpc in diameter and a molecular gas reservoir of ~5 x 10^{11} M_solar.
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