  We analyse the Planck full-mission cosmic microwave background (CMB)
temperature and E-mode polarization maps to obtain constraints on primordial
non-Gaussianity (NG). We compare estimates obtained from separable
template-fitting, binned, and modal bispectrum estimators, finding consistent
values for the local, equilateral, and orthogonal bispectrum amplitudes. Our
combined temperature and polarization analysis produces the following results:
f_NL^local = -0.9 +\- 5.1; f_NL^equil = -26 +\- 47; and f_NL^ortho = - 38 +\-
24 (68%CL, statistical). These results include the low-multipole (4 <= l < 40)
polarization data, not included in our previous analysis, pass an extensive
battery of tests, and are stable with respect to our 2015 measurements.
Polarization bispectra display a significant improvement in robustness; they
can now be used independently to set NG constraints. We consider a large number
of additional cases, e.g. scale-dependent feature and resonance bispectra,
isocurvature primordial NG, and parity-breaking models, where we also place
tight constraints but do not detect any signal. The non-primordial lensing
bispectrum is detected with an improved significance compared to 2015,
excluding the null hypothesis at 3.5 sigma. We present model-independent
reconstructions and analyses of the CMB bispectrum. Our final constraint on the
local trispectrum shape is g_NLl^local = (-5.8 +\-6.5) x 10^4 (68%CL,
statistical), while constraints for other trispectra are also determined. We
constrain the parameter space of different early-Universe scenarios, including
general single-field models of inflation, multi-field and axion field
parity-breaking models. Our results provide a high-precision test for
structure-formation scenarios, in complete agreement with the basic picture of
the LambdaCDM cosmology regarding the statistics of the initial conditions
(abridged).
