The total energy $E=mc^2/\sqrt{1-v^2/c^2}$ contains the rest energy $mc^2$ and a kinetic part $T(v)=E(v)-mc^2$. In you reference frame there is no kinetic part. (Your formulas are wrong.) And the relativistic formula for $E$ is valid for neutral particles too.

The radiated energy depends on the particle charge, its velocity and acceleration. The notion of electromagnetic mass is misleading. There is a mass defect, which is real for compound "particles", but the rest energy is not of purely electromagnetic nature. Annihilation of electron and positron may occur to a couple of neutral particles other than photons, to a couple of neutrino and antineutrino, for example, i.e., via weak interaction.

Apart from the radiated field, there is a "near" field following the particle. The corresponding formulas for this field for a uniformly moving charge are given in textbooks.