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We present the results from our Atacama Large Millimeter/submillimeter Array (ALMA) imaging observations of the CO (7−6), [C i] 370 µm (hereafter [C i]) and [N ii] 205 µm (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 ∼1.1 ′′ to 1.2 ′′ (or 7.5 to 8.2 kpc), the continuum at 205 and 372 µm (restframe), 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 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 −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 L CO(7−6) /L FIR luminosity ratio is consistent with that of local luminous infrared galaxies powered predominantly by SF. The L CO(7−6) -inferred SF rate is 5.1 (±1.5) × 10 3 M ⊙ yr −1 . 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 × 10 11 M ⊙ .