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The low-frequency linearly polarised radio source population is largely unexplored. However, a renaissance in low-frequency polarimetry has been enabled by pathfinder and precursor instruments for the Square Kilometre Array. In this second paper from the POlarised GaLactic and Extragalactic All-Sky MWA Survey-the POlarised GLEAM Survey, or POGS-we present the results from our all-sky MWA Phase I Faraday Rotation Measure survey. Our survey covers nearly the entire Southern sky in the Declination range 
$-82^\circ$
to 
$+30^\circ$
at a resolution between around three and seven arcminutes (depending on Declination) using data in the frequency range 169−231 MHz. We have performed two targeted searches: the first covering 25 489 square degrees of sky, searching for extragalactic polarised sources; the second covering the entire sky South of Declination 
$+30^\circ$
, searching for known pulsars. We detect a total of 517 sources with 200 MHz linearly polarised flux densities between 9.9 mJy and 1.7 Jy, of which 33 are known radio pulsars. All sources in our catalogues have Faraday rotation measures in the range 
$-328.07$
to 
$+279.62$
rad m−2. The Faraday rotation measures are broadly consistent with results from higher-frequency surveys, but with typically more than an order of magnitude improvement in the precision, highlighting the power of low-frequency polarisation surveys to accurately study Galactic and extragalactic magnetic fields. We discuss the properties of our extragalactic and known-pulsar source population, how the sky distribution relates to Galactic features, and identify a handful of new pulsar candidates among our nominally extragalactic source population.
We present a detailed analysis of the radio galaxy PKS 
$2250{-}351$
, a giant of 1.2 Mpc projected size, its host galaxy, and its environment. We use radio data from the Murchison Widefield Array, the upgraded Giant Metre-wavelength Radio Telescope, the Australian Square Kilometre Array Pathfinder, and the Australia Telescope Compact Array to model the jet power and age. Optical and IR data come from the Galaxy And Mass Assembly (GAMA) survey and provide information on the host galaxy and environment. GAMA spectroscopy confirms that PKS 
$2250{-}351$
lies at 
$z=0.2115$
in the irregular, and likely unrelaxed, cluster Abell 3936. We find its host is a massive, ‘red and dead’ elliptical galaxy with negligible star formation but with a highly obscured active galactic nucleus dominating the mid-IR emission. Assuming it lies on the local M–
$\sigma$
relation, it has an Eddington accretion rate of 
$\lambda_{\rm EDD}\sim 0.014$
. We find that the lobe-derived jet power (a time-averaged measure) is an order of magnitude greater than the hotspot-derived jet power (an instantaneous measure). We propose that over the lifetime of the observed radio emission (
${\sim} 300\,$
Myr), the accretion has switched from an inefficient advection-dominated mode to a thin disc efficient mode, consistent with the decrease in jet power. We also suggest that the asymmetric radio morphology is due to its environment, with the host of PKS 
$2250{-}351$
lying to the west of the densest concentration of galaxies in Abell 3936.
