Electromagnetism and Feynman diagrams

[Ray]

1. Feynman says all of electromagnetism follows from Maxwell equations.
2. Somebody (Pointing to a Feynman diagram of a photon/electron reaction) said all of electromagnetism is in that one diagram. So, can anyone help me with these two questions: how does point 1 come from point 2. And, how does a photon come from an EM field just by using it in a Langragian form?

 

[jostpuur]

I remember when I asked one particle physicists, that "how does Coulomb's force follow from that diagram?". The response was "no... we use these to calculate particle collision cross-sections". That's the unpleasant, but simple, truth You are not getting electromagnetism out of particle exchanges.