  [Abridged] We present new optical integral field spectroscopy (Gemini South)
and submillimeter spectroscopy (Submillimeter Array) of the central galaxy in
the Phoenix cluster (SPT-CLJ2344-4243). This cluster was previously reported to
have a massive starburst (~800 Msun/yr) in the central, brightest cluster
galaxy, most likely fueled by the rapidly-cooling intracluster medium. These
new data reveal a complex emission-line nebula, extending for >30 kpc from the
central galaxy. The total Halpha luminosity, assuming Halpha/Hbeta = 2.85, is
L_Ha = 7.6 +/- 0.4 x10^43 erg/s, making this the most luminous emission line
nebula detected in the center of a cool core cluster. Overall, the relative
fluxes of the low-ionization lines (e.g., [O II], Hbeta) to the UV continuum
are consistent with photoionization by young stars. In both the center of the
galaxy and in a newly-discovered highly-ionized plume to the north of the
galaxy, the ionization ratios are consistent with both shocks and AGN
photoionization. We speculate that this extended plume may be a galactic wind,
driven and partially photoionized by both the starburst and central AGN. We
find evidence for shocks throughout the ISM of the central galaxy, most likely
driven by a combination of stellar winds from massive young stars,
core-collapse supernovae, and the central AGN. In addition to the warm, ionized
gas, we detect a substantial amount of cold, molecular gas via the CO(3-2)
transition, coincident in position with the galaxy center. We infer a molecular
gas mass of M_H2 = 2.2 +/- 0.6 x10^10 Msun, which implies that the starburst
will consume its fuel in ~30 Myr if it is not replenished. The combination of
the high level of turbulence in the warm phase and the high L_IR/M_H2 ratio
suggests that this violent starburst may be in the process of quenching itself.
