When you understand the electron you understand mass. Then when you take the next steps you can understand electron capture and beta decay.
I'm not so sure about this. The electron is a special manifestation of charge. Inside the nucleus the mass associated with charge sometime doubles (neutron case). Without understanding how charge is generated you will not manage to understand the electron.
The picture of the photon being a sinus wave is wrong as there is no chance that E/B field are 0 at the same moment. This would imply that the energy is stored in a fantastic medium called ether that should exhibit its property absolutely symmetric to a wave. Better classic pictures show the E/B wave field with a 90o offset (phase). Now it's up to you to find the true angle between E,B wave.