The mass and meson- current coupling of the diquark- antidiquark states with the quantum numbers J(P) = 0(+) and quark contents Z(q) = [cq] [(b) over bar (q) over bar] and Z(s) = [cs] [(b) over bar(s) over bar] are calculated using the two- point QCD sum rule approach. In calculations the quark, gluon, and mixing condensates up to eight dimensions are taken into account. The parameters of the scalar tetraquarks extracted from this analysis are employed to explore the strong vertices Z(q)B(c)pi, Z(q)B(c)eta, and Z(s)B(c) eta and compute the couplings gZ(q)B(c)pi, gZ(q)B(c)eta, and gZ(s)B(c) eta. The strong couplings are obtained within the soft- meson approximation of the QCD light- cone sum rule method: they form, alongside with other parameters, the basis for evaluating the widths of Z(q) -> B-c pi, Z(q) -> B-c eta, and Z(s) -> B-c eta decays. Results obtained in this work for the mass of the tetraquarks Z(q) and Z(s) are compared with available predictions presented in the literature.