How is oscillation of EM waves determined in cases that don't involve accelerating charges in a/c currents If the frequency of an electromagnetic wave equals the frequency of oscillation of the (source) charge producing it, what about in the case where the accelerating source charge is not oscillating (changing direction) but, instead, is moving in only one direction? After all, the source charge is still accelerating if it's changing speed (for example, EMR emitted when electrons fall to lower energy levels).
 A: You can still decompose its movement in a Fourier transform. The resulting spectrum equals the frequencies emitted.
A: Mathematically, any function may be decomposed into periodic sinusoids via Fourier analysis. What we observe in nature corresponds to this math. A prism will separate light into colors representing the Fourier components of the light. Via the Planck relation, the Fourier power predicts the probability of observing a photon with a given energy. There are many other examples.
A: There are three phenomena you mention and I start from the end of the list: EM radiation from excited electrons, EM radiation from electrons in a circular motion and EM waves from oscillating electrons.
An electron excited in the atom emits photons. It is important to emphasize that the understanding of EM radiation as an emission of quanta found by Planck and Einstein is a fundamental one. All EM radiation consists of these corpuscles.
Deflected electrons also emit electrons. The only condition is that they have a kinetic energy, because this energy is transformed into EM radiation. The deflection can be a circular motion forced by a coil or by an external magnet. Here is still important the understanding that the (forced, and otherwise this movement also does not exist) circular movement for the electrons represent an acceleration, because every circular movement is an acceleration.
The synchronous and oscillatory acceleration of surface electrons in a conductor represents a special case of the emission of photons. The emitted photons have their peak at the times of the largest acceleration values and a zero value at the time with zero acceleration. Perhaps it is worth mentioning that the photons emitted in this way are polarized, i.e. their electric field components are all aligned parallel to the conductor (with changing sign depending on the direction of acceleration). Thus, kinetic energy is also converted into radiation here.
So, as you can see, the emission of excited electrons in the atom is the process that is not associated with acceleration. It is a process in which absorbed photons lead to the raising of the energy level and photons are emitted again at the relaxation.
