We present improved estimates of the couplings, masses and mass ratios of the $Z_Q,X_Q$ and $T_{QQ\overline{q}{\overline{q}}^{\prime }}$ states ($Q\equiv c,b;q,q^{\prime }\equiv u,d,s$) using (inverse) QCD Laplace sum rules (LSR), their ratios $\mathcal{R}$ 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 $\overline{MS}$ heavy quark mass used in the analysis. We show that combined $\mathcal{R}$ 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: $M_{{\mathcal{T}}_{X_c}}=3876(44)\text{MeV}$ and $M_{{\mathcal{T}}_{Z_c}}=3900(42)\text{MeV}$. In the 2nd part, we focus on the analysis of the four-quark nature of different $T_{QQ\overline{q}{\overline{q}}^{\prime }}$$1^{+}$ and $0^{+}$ states within the ${\overline{3}}_c{3}_c$ interpolating currents. The final results from $\mathcal{R}$ and $\mathcal{R}\oplus$ DRSR are summarized in Table 7. Combined $\mathcal{R}$ and DRSR calibrated to the observed $X_c(3872)$ lead to a precise prediction of e.g. $M_{T_{cc}^{1^{+}}}=3886(6)\text{MeV}$. In a similar way, the DRSR for the $M_{T_{cc}^{0^{+}}}/M_{T_{cc}^{1^{+}}}$ calibrated to $M_{T_{cc}^{1^{+}}}$ gives $M_{T_{cc}^{0^{+}}}=3883(3)\text{MeV}$. The SU3 breaking ratios $M_{T_{cc\overline{s}\overline{s}}^{0^{+}}}/M_{T_{cc}^{0^{+}}}$ lead to the improved mass predictions: $M_{T_{cc\overline{s}\overline{s}}^{0^{+}}}=3988(12)\text{MeV}$. In the 3rd part, the analysis is extended to the beauty mesons, where we find the tetramole masses: $M_{{\mathcal{T}}_{Z_b}}=10579(99)\text{MeV}$ and $M_{X_b}=10545(131)\text{MeV}$. We also observe that the $T_{bb\overline{q}{\overline{q}}^{\prime }}^{1^{+},0^{+}}$ ($q,q^{\prime }\equiv u,d,s$) 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 $T_{QQ\overline{q}{\overline{q}}^{\prime }}^{1^{+},0^{+}}$ masses. Our combined LSR ⊕ DRSR results are confronted with the ones from some other approaches (lattices and quark models) in Fig. 26.