We report new Northern Extended Millimeter Array observations of the [C ii ] _{158 μ m} , [N ii ] _{205 μ m} , and [O i ] _{146 μ m} atomic fine structure lines (FSLs) and dust continuum emission of J1148+5251, a z = 6.42 quasar, which probe the physical properties of its interstellar medium (ISM). The radially averaged [C ii ] _{158 μ m} and dust continuum emission have similar extensions (up to θ = 2.51 − 0.25 + 0.46 arcsec , corresponding to r = 9.8 − 2.1 + 3.3 kpc , accounting for beam convolution), confirming that J1148+5251 is the quasar with the largest [C ii ] _{158 μ m} -emitting reservoir known at these epochs. Moreover, if the [C ii ] _{158 μ m} emission is examined only along its NE–SW axis, a significant excess (>5.8 σ ) of [C ii ] _{158 μ m} emission (with respect to the dust) is detected. The new wide-bandwidth observations enable us to accurately constrain the continuum emission, and do not statistically require the presence of broad [C ii ] _{158 μ m} line wings that were reported in previous studies. We also report the first detection of the [O i ] _{146 μ m} and (tentatively) [N ii ] _{205 μ m} emission lines in J1148+5251. Using FSL ratios of the [C ii ] _{158 μ m} , [N ii ] _{205 μ m} , [O i ] _{146 μ m} , and previously measured [C i ] _{369 μ m} emission lines, we show that J1148+5251 has similar ISM conditions compared to lower-redshift (ultra)luminous infrared galaxies. CLOUDY modeling of the FSL ratios excludes X-ray-dominated regions and favors photodissociation regions as the origin of the FSL emission. We find that a high radiation field (10 ^3.5–4.5 G ₀ ), a high gas density ( n ≃ 10 ^3.5–4.5 cm ⁻³ ), and an H i column density of 10 ²³ cm ⁻² reproduce the observed FSL ratios well.