If particles are excitations what are their fields?

After reading these :

1. http://www.symmetrymagazine.org/article/july-2013/real-talk-everything-is-made-of-fields


2. http://www.physicsforums.com/showthread.php?t=682522

It was clear to me that all particles are merely excitation in fields. But it caused a few questions

1. If electron is excitation in electron field, then how does it produce it's own field?


2. For whatever reason electron even after being an excitation produces an electric field, but why doesn't photon (or other such particles if there are) create any such field?


3. All these particles have mass and exert gravity how can they produce gravitational fields?

The major question that partly summarises all three of them has to be " when particles are excitation in some field how do fields arise from them? "