We present improved estimates of the couplings, masses and mass ratios of the Z Q , X Q and T QQq q states (Q ≡ c, b ; q, q ≡ u, d, s) using (inverse) QCD Laplace sum rules (LSR), their ratios R and double ratios DRSR within stability criteria, where the NLO factorized PT QCD corrections are included which is important for giving a meaning on the running M S heavy quark mass used in the analysis. We show that combined R and DRSR can provide more precise results. In the 1st part of the paper, we conclude that the observed X c (3872) and Z c (3900) are tetramoles states (superposition of quasi-degenerated molecule and a tetraquark states having (almost) the same coupling to the currents) with the predicted masses : M T Xc = 3876(44) MeV and M T Zc = 3900(42) MeV. In the 2nd part, we focus on the analysis of the four-quark nature of different T QQq q 1 + and 0 + states within the 3c 3 c interpolating currents. The final results from R and R ⊕ DRSR are summarized in Table 7. Combined R and DRSR calibrated to the observed X c (3872) lead to a precise prediction of e.g. M T 1 + cc =3886(6) MeV. In a similar way, the DRSR for the(3) MeV. The SU3 breaking ratios M T 0 + ccss /M T 0 + cc lead to the improved mass predictions : 12) MeV. In the 3rd part, the analysis is extended to the beauty mesons, where we find the tetramole masses : M T Z b = 10579(99) MeV and M X b = 10545(131) MeV. We also observe that the T 1 + ,0 + bbq q (q, q ≡ u, d, s) states are (almost) stable (within the errors) against strong interactions. In the 4th part, we (critically) review and correct some recent LSR estimates of the T 1 + ,0 + QQq q masses. Our combined LSR ⊕ DRSR results are confronted with the ones from some other approaches (lattices and quark models) in Fig. 25.