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 \sim 1.1″ to 1.2″ ( or 7.5 to 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 de-convolved major axis of 1.3″ ( \pm 0.3″ ) or 9 ( \pm 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 ( \pm 1.5 ) \times 10 ^ { 3 } M _ { \odot } 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 \sim 5 \times 10 ^ { 11 } M _ { \odot } .