  We present improved estimates of the couplings, masses and mass ratios of the
Z_Q,X_Q and T_{QQqq} states using 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 MS heavy quark mass used in the analysis. We show that combined R and
DRSR can provide more precise results. First, 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_{X_c}}=3876(44) MeV
and M_{ T_{Z_c}}=3900(42) MeV. In the 2nd part, we focus on the analysis of the
four-quark nature of different T_{QQqq'} 1^+ and 0^+ states within the 3_c3_c
interpolating currents. The final results 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_{cc}^{1^+}}=3886(6) MeV. In a similar way, the DRSR for
M_{T_{cc}^{0^+}}/M_{T_{cc}^{1^+}} calibrated to M_{T_{cc}^{1^+}} gives
M_{T_{cc}^{0^+}}= 3883(3) MeV. The SU3 breaking ratios M_{T_{ccss}^{0^+}}/
M_{T_{cc}^{0^+}} lead to the improved mass predictions:
M_{T_{ccss}^{0^+}}=3988(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^+}_{bbqq'}
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^+}_{QQqq'} masses. Our results from LSR+DRSR are confronted with
the ones from some other approaches (lattices and quark models) in Fig. 25.
