I tried to reorder your questions to provide a more coherent answer. The answers are not very simple, and I will try my best to present them as clearly as possible. Physicists accelerate electrically charged particles, increasing the energy of these particle. Once forces or collisions occur, a particle may emit a photon while satisfying the law of energy conservation.
Acceleration is nothing else but a force acting on a particle.
The amount of energy in form of light that an accelerated particle may emit depends on the direction in which the acceleration occurs. In the case of acceleration in direction of motion, only very little energy may be emitted. As a matter of fact, the forward acceleration provided by today's most powerful accelerators is not sufficient to create radiation. The perpendicular acceleration, created by, for example, the magnets in circular accelerator, allows for much more light to be emitted. This light, also called synchrotron light, is produced by all ring-shaped accelerators around the world.