We present 168 arcmin^2 spectral images of the Sgr B2 complex taken with Herschel/SPIRE-FTS. We detect ubiquitous emission from CO (up to J=12-11), H2O, [CI]492, 809 GHz, and [NII] 205 um lines. We also present maps of the SiO, N2H+, HCN, and HCO+ emission obtained with the IRAM30m telescope. The cloud environment dominates the emitted FIR (80%), H2O 752 GHz (60 %) mid-J CO (91%), and [CI] (93 %) luminosity. The region shows very extended [NII] emission (spatially correlated with the 24 and 70 um dust emission). The observed FIR luminosities imply G_0~10^3. The extended [CI] emission arises from a pervasive component of neutral gas with n_H~10^3 cm-3. The high ionization rates, produced by enhanced cosmic-ray (CR) fluxes, drive the gas heating to Tk~40-60 K. The mid-J CO emission arises from a similarly extended but more pressurized gas component (P_th~10^7 K cm-3). Specific regions of enhanced SiO emission and high CO-to-FIR intensity ratios (>10^-3) show mid-J CO emission compatible with shock models. A major difference compared to more quiescent star-forming clouds in the disk of our Galaxy is the extended nature of the SiO and N2H+ emission in Sgr B2. This can be explained by the presence of cloud-scale shocks, induced by cloud-cloud collisions and stellar feedback, and the much higher CR ionization rate (>10^-15 s-1) leading to overabundant H3+ and N2H+. Hence, Sgr B2 hosts a more extreme environment than star-forming regions in the disk of the Galaxy. As a usual template for extragalactic comparisons, Sgr B2 shows more similarities to ultra luminous infrared galaxies such as Arp 220, including a deficit in the [CI]/FIR and [NII]/FIR intensity ratios, than to pure starburst galaxies such as M82. However, it is the extended cloud environment, rather than the cores, that serves as a useful template when telescopes do not resolve such extended regions in galaxies.
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