  This paper is the third in a series in which we present deep Chandra ACIS-S
imaging spectroscopy of the Seyfert 1 galaxy NGC 4151, devoted to study its
complex circum-nuclear X-ray emission. Emission features in the soft X-ray
spectrum of the bright extended emission (L[0.3-2keV]~10^40 erg/s) at r>130 pc
(2") are consistent with the brighter OVII, OVIII, and NeIX lines seen in the
Chandra HETGS and XMM-Newton RGS spectra below 2 keV. We construct emission
line images of these features and find good morphological correlations with the
narrow line region clouds mapped in [OIII]5007A. Self-consistent
photoionization models provide good descriptions of the spectra of the large
scale emission, as well as resolved structures, supporting the dominant role of
nuclear photoionization, although displacement of optical and X-ray features
implies a more complex medium. Collisionally ionized emission is estimated to
be <12% of the extended emission. Presence of both low and high ionization
spectral components and extended emission in the X-ray image perpendicular to
the bicone indicates leakage of nuclear ionization, likely filtered through
warm absorbers, instead of being blocked by a continuous obscuring torus. The
ratios of [OIII]/soft X-ray flux are approximately constant (~15) for the 1.5
kpc radius spanned by these measurements, indicating a relatively constant
ionization parameter, consistent with the photoionized outflow of a wind-like
density profile. Using spatially resolved features, we estimate that the mass
outflow rate in NGC 4151 is ~2Msun/yr at 130 pc and the kinematic power of the
ionized outflow is 1.7x10^41 erg/s, approximately 0.3% of the bolometric
luminosity of NGC 4151.
