1. The theory of the two-dimensional (2D) magnetoexcitons was completed taking into account the electron-hole (e-h) exchange Coulomb interaction, which appears when the conduction (c) and the valence (v) electrons and holes belong partially to both bands, when the Coulomb interaction between them has a dipole-dipole character, and the interband dipole moment c v r - does not vanish. In this case the para-magnetoexciton state is dipole-active and bright. Due to the action of the Lorentz force there is a strong inter-dependence between the relative e-h and center-of-mass motions and the Coulomb exchange interaction leads to linear dispersion of the magnetoexcitons. The Dirac cone dispersion law is characterized by the group velocity g v with the dependence γg ~I   ρ _{c v}  - /l₀I² ~ B where 0 l is the magnetic length and B is the magnetic field strength. The thermodynamic properties of the 2D ideal Bose gas were studied [1], taking into account that the critical temperature c T of the Bose-Einstein condensation is proportional to the group velocity Tc ~ γg ~ B and is different from zero. 2. The possible existence of the bound states of the interacting 2D magnetoexcitons with in-plane opposite wave vectors k and -k , as well as with antiparallel electric dipole moments oriented perpendicularly to the corresponding wave vectors was investigated in the lowest Landau levels (LLLs) approximation. Four definite spin structures of the two electrons and of two holes forming the molecule were taken into account. Two of them named as singlet-singlet and triplet-triplet concern to the spin orientations of the two electrons and of the two holes separately, whereas another two are related with the spin structure of two para- and of two ortho-magnetoexcitons. In the last case the three spin projections of the each ortho-magnetoexciton as well as the resultant spin equal to zero of the both magnetoexcitons forming the molecule were taken into account. Two variational wave functions describing the relative motion of two magnetoexcitons in the frame of molecule were used. It was shown that the stable bound states of the bimagnetoexcitons in the LLLs approximation do not exist. Instead, a metastable bound state in the case of the triplet-triplet spin configuration with the activation energy barrier comparable with the magnetoexciton ionization potential l I was revealed. 3. It was shown that the Chern-Simons (C-S) gauge field created by the quantum point vortices in the conditions of the fractional quantum Hall effects (FQHEs) leads to the formation of the composite electrons and holes with equal integer numbers of the attached to each particle quantum point vortices. The coherent superposition of the velocities of these vortices leads to the formation of the C-S vector potential, which depends on the difference between the density operators ˆe r of the electrons and ˆh r of the holes. The C-S vector potential generates the effective magnetic field acting on the particles in addition to the external magnetic field. In the mean field approximation, when the average densities of electrons and of the holes coincide the effective C-S magnetic and electric fields vanish and the Landau quantization of the composite particles with the bare electron and hole effective masses take place only under the influence of the external magnetic field.