  Radio continuum observations at 1.4, 4.8 and 8.6 GHz of the two Planetary
Nebulae (PNe) in the Sagittarius dwarf galaxy reveal the elongated shape of
Wray 16-423 and the extreme compactness of He 2-436. He 2-436 is confirmed as
subject to local dust extinction.
  Photoionization models for both PNe are obtained from two different codes,
allowing theoretical uncertainties to be assessed. Wray 16-423, excited by a
star of Teff 1.07x10^5K, is an ellipsoidal, matter-bounded nebula, except for a
denser sector. He 2-436, excited by a 7x10^4K star, includes two
radiation-bounded shells, with the inner one possibly corresponding to a
transitory event. Both stars are on the same (H-burning) evolutionary track of
initial mass (1.2+/-0.1) Msun and may be twins, with the PN ejection of Wray
16-423 having occured ~1500 years before He 2-436.
  The PN abundances re-inforce the common origin of the parent stars,
indicating almost identical depletions with respect to solar for O, Ne, Mg, S,
Cl, Ar, and K (-0.55+/-0.07 dex), large identical overabundances for He and
strong overabundances for carbon, particularly in He2-436. Excess nitrogen
makes Wray 16-423 nearly a Type I PN. These PNe provide a means to calibrate
both metallicity and age of the Sagittarius stellar population, and they
confirm that the youngest, most metal-rich population has an age of 5Gyr and a
metallicity of [Fe/H]=-0.55, in agreement with the slope of the red giant
branch. (Abridged abstract)
