As you can see in these diagrams, they radiate these virtual photons. The virtual photons have no charge or mass, and there is no apparent visible change in the energy of the electron after it radiates this photon. I'm aware that the probability level of the incident occurring drops by 1% for every extra vertex in the diagram, so low as the probability can get, it can never touch 0. What stops the electron from radiating multiple photons that can turn into other particles? What change occurs in the electron itself after the emission of the photon?
My understanding is that this is due to momentum conservation.
A gamma ray cannot create an e-/e+ pair without interacting with a nucleus in order to conserve momentum. This is why the virtual gamma ray here can only create a virtual (off-shell) e-/e+ pair.
The change that occurs in the electron after the photon emission is just a change in energy/momentum.
Additionally, your comment about an electron creating multiple gammas - the only vertex allowed is two fermions with a photon, so emitting multiple gammas must be done in the fashion shown in the first diagram (in multiple steps)