  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.
