The possible existence of bound states of the interacting two-dimensional (2D) magnetoexcitons with different spinstructures in the lowest Landau levels (LLLs) approximation was investigated using the Landau gauge description. Themagnetoexcitons taking part in the formation of the bound state with resultant wave vector k = 0 have opposite in-plane wave vectors k and –k and look as two electric dipoles with the arms oriented in-plane perpendicularly to thecorresponding wave vectors. The length of the arms equals to 20 d = kl , where 0 l is the magnetic length. The bound state oftwo antiparallel dipoles moving with equal but antiparallel wave vectors in any direction of the plane with equal probabilityis characterized by the variational wave function of the relative motion ( ) n  k depending on the modulus | k | .The magnetoexcitons are composed of electrons and holes situated on the LLLs with cyclotron energies greater than the bindingenergies of the 2D Wannier-Mott exciton, and interact through the Coulomb interactions of their constituents.The spins of the electrons and the effective spins of two holes forming the bound states were combining separately in thesymmetric or in the antisymmetric forms (   ) with the same parameter  = 1 for electrons and holes. Two typesof wave functions, one with singlet electron and singlet hole structure and another one with triplet electron and triplet holestructure were used, leading to completely different bound states. The mixt states of the type singlet electrons and triplethole or vice versa do not exist due to the hidden symmetry of the electron and hole in the lowest Landau levels in theLandau gauge description. Because the projections of the both spinor states with  = 1 are equal to zero, the effect of theZeeman splitting vanishes. The para and ortho magnetoexciton states up till now were not investigated and the splitting oftheir energy levels is unknown at present time.In the case of the variational wave function 2 23 1 2 2 2 02 0  (k) = (8 ) k l e- k l the maximum density of the magnetoexcitons in themomentum space representation is concentrated on the in-plane ring with the radius 0 1 ( ). rk = l  In the LLLsapproximation, when the influence of the excited Landau levels (ELLs), as well as of the Rashba spin-orbit coupling(RSOC) are neglected, the stable bound states of the bimagnetoexciton molecule do not exist for both spin orientations.Instead of them, a deep metastable bound state with the activation barrier comparable with double ionization potentials 2 l Iof the magnetoexciton with k = 0was revealed in the case  = 1 and  = 0.5 . In the case  = -1 and  = 3.4 only ashallow metastable bound state can appear. In the case of the variational wave function 2 21 2 00 (k) = (4 ) e- k l all the boundstates are unstable and the molecule bimagnetoexciton cannot be formed in the LLLs approximation.The energy spectrum of the two-dimensional cavity magnetoexciton-polaritons was investigated. The effective polaritonmass on the lower polariton branch, the Rabi frequency and the corresponding Hopfield coefficients were determined independence on the magnetic field strength and on the Rashba spin-orbit coupling parameters.Supplementary to the Ref. [1], new results concerning the Zeeman splitting effects at different values of the electron andhole g-factors were investigated.[1] Sveatoslav A. Moskalenko, Igor V. Podlesny, Evgheni V. Dumanov, Michael A. Liberman, and Boris V. Novikov,Journal of Nanophotonics, 10(3), 036006 (2016), http://dx.doi.org/10.1117/1.JNP.10.036006