An electron at rest has 511 keV of energy, which is ~10^6 times the energy of visible light (~1 eV), so from energy considerations alone it has more than enough to "create" a photon. Accelerating electrons are a great source of light via Bremsstrahlung and synchrotron radiation.

This is the fundamental reason why electrons can't orbit the nucleus in a classical sense (and why we know the Bohr model is incorrect). The atom is a quantum object and as such it does not behave in a classical manner. You can describe it heuristically as an electron 'orbiting' the nucleus but that is not what's actually happening. The very concept of a path or trajectory does not have any meaning for quantum objects, which exist in probabilistic quantum states.