The tree-level two-point amplitudes for the transitions $jf to j^{, prime} f^{, prime}$, where $f$ is a fermion and $j$ is a generalized current, in a constant uniform magnetic field of an arbitrary strength and in charged fermion plasma, for the $jf
$ interaction vertices of the scalar, pseudoscalar, vector and axial-vector types have been investigated. The particular cases of a very strong magnetic field, and of the coherent scattering off the real fermions without change of their states (the forward scattering) have been analysed.
The process of photon splitting is investigated in the presence of strongly magnetized electron-positron plasma. The amplitude of the process is calculated in general case of plasma with nonzero chemical potential and temperature. The polarization se
lection rules and corresponding partial amplitudes for allowed splitting channels are obtained in the case of charge-symmetric plasma. It is found that the new splitting channel forbidden in magnetized vacuum becomes allowed. The absorption rates of the photon splitting are calculated with taking into account of the photon dispersion and wave function renormalization. In addition, the comparison of photon splitting and Compton scattering process is made. The influence of the reactions under consideration on the radiation transfer in the framework of magnetar model of SGR burst is discussed.
