Are photons emitted and absorbed in a direction mostly perpendicular to the acceleration of a charge? In classical electrodynamics books, I always see the radiation as perpendicular to the acceleration of an electric charge.  For example in cyclotron radiation, and in antenna radiation.
However, intuitively based on looking at feynman diagrams, I would expect that photons should be emitted and absorbed at a 180' orientation to the electron acceleration not at a 90' angle based on conservation of momentum.
Is there a difference between the angle of emission and absorption for single particle vs multiparticle events and should that angle not be 180' to the change in acceleration instead of 90'?
 A: As Anna V and G Smith say, if you want an exact answer you calculate the Feynman diagram - but you don't use it as a physical picture because it isn't.
If you do the calculation you will, in most cases I've met, find the photon direction peaks along the direction of the original charge and the direction of the outgoing struck charge.
And there is an intuitive explanation for this: when a charged particle moves it is not just a mass but the centre of a moving electric and magnetic fields. If you looked at it closely you would see a particle accompanied by a whole bunch of virtual photons and this bunch of photons is travelling along with the particle, in about the same direction at about the same speed. If something (such as a nuclear charge) disturbs that particle from its trajectory it doesn't take much for one of those virtual photons moving along the particle trajectory to become real, and that's the emitted photon you see.
Synchrotron radiation is a good example of this.
A: Here is the Feynman diagram

As you see the process is not just an electron and a photon, there has to be a virtual photon, in this case with a nucleus, (in the acceleration case  provided by the field)  and a virtual electron in the diagram;  . So there are more variables and the angle of emission will follow the probability distribution  from the calculation of the diagram.

Are photons emitted and absorbed in a direction mostly perpendicular to the acceleration of a charge?

As there is continuity between classical and quantum mechanical solutions, and as the classical emerges from the quantum mechanical, the probability distribution of the photons should build collectively  up the classical distribution
The way individual photons add up to a classical electromagnetic wave is not simple, can be seen with quantum field theory terms, see this link. For me an intuitive understanding between classical electromagnetism and photons which are quantum mechanical entities came from looking at this image
A: If you consider the electric part of an electromagnetic wave as a transverse distortion introduced into a preexisting electric field, then the field strength should drop off with the cosine of the angle measured from the perpendicular to the line of oscillation of the charge.
