We present the results from our Atacama Large Millimeter/submillimeter Array (ALMA) imaging observations of the CO(7-6), [C I] 370 mu m (hereafter [C I]), and [N II] 205 mu m (hereafter [N II]) lines and their underlying continuum emission of BRI 1335-0417, an infrared bright quasar at z = 4.407. At the achieved resolutions of similar to 1.'' 1 to 1.'' 2 (or 7.5-8.2 kpc), the continuum at 205 and 372 mu m (rest frame), the CO(7-6), and the [C I] emissions are at best barely resolved whereas the [N II] emission is well resolved with a beam-deconvolved 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 500-600 km s(-1). The far-infrared (FIR) dust temperature (T-dust) of 41.5 K from a graybody fit to the continuum agrees well with the average T-dust inferred from various line luminosity ratios. The resulting LCO(7-6)/L-FIR luminosity ratio is consistent with that of local luminous infrared galaxies powered predominantly by SF. The LCO(7-6)-inferred SF rate is 5.1(+/- 1.5) x 10(3) M-circle dot yr(-1). The system has an effective star-forming region of 1.7(-0.8)(+1.7) kpc in diameter and a molecular gas reservoir of similar to 5 x 10(11) M-circle dot.