  We discuss the topics mentioned in the title by scrutinizing and improving
the $0^{-+}$ di-gluonia sum rules within the standard SVZ-expansion at N2LO
without instantons. First, we reconsider the estimate of the slope of the
topological charge $\chi'(0)=24.3(3.4)$ MeV which imply $0.144(5) [\rm data:
0.145(13)]$ for the first moment of the polarized proton structure function
(proton spin) and $G_A^{(0)} = 0.337(50) [\rm data=0.330(39)]$ for the singlet
form factor of the axial current. Second, we work with high degree moments and
parametrize the spectral function beyond the minimal duality ansatz: "One
resonance plus QCD continuum" to get the $0^{-+}$ di-gluonia spectra. Then, we
obtain three groups of gluonia: The familiar light $\eta_1$ [singlet gluon
component of the $\eta'(958)$] with $[M_{\eta_1},f_{\eta_1}]= [825 , 905(72)]$;
The two new medium gluonia with $M_{P_{1a}}=1338(112)$ MeV and
$[M_{P_{1b}}=1462(117) $ MeV or their mean
$[M_{P_1},f_{P_1}]=[1397(81),594(144)]$ MeV which support the gluonium nature
of the candidate $\eta(1405)$ and may bring a small gluon piece to the
$\eta(1295)$; Their 1st radial excitations: $M_{P'_{1a}}=1508(226)$ MeV and
$M_{P'_{1b}}=1553(139)$ MeV with their mean:
$[M_{P'_1},f_{P'_1}]=[1541(118),205(282)]$ MeV which may be identified (up to
some eventual mixings with $\bar qq$ states) with the $\eta(1475,1700)$ states;
The heavy gluonium with : $[M_{P_2}, f_{P_2}]=[2751(140),500(43)]$ MeV
comparable with the lattice results. One can remark the (natural) one to one
correspondence between the pseudoscalar gluonia and their chiral scalar
analogue from Ref.1: $\sigma(1)\to \eta_1;~G_1(1.55)\to P_{1};
[\sigma'(1.1),G'(1.56)]\to P'_{1a,1b};~G_2(3)\to P_2$ which is mainly due to
the importance of QCD PT in the sum rule analysis that are almost equal in
these two channels. Results for the spectra are in Table 2.
