electric field is a "form of matter" and … I really want to know what made it.
Electric fields are not made, they simply exist. Every electron and every proton has an elementary electric charge. And, by the way, also an intrinsic magnetic dipole. We don't notice any of this, because these fields usually balance each other out.
We get a macroscopic electric field through a charge separation. On one side we create an electron excess and on the other side an electron deficiency.
And finally, I want to know the process of the transfer of the interaction of two charges.
Physics deals with virtual photons that are exchanged in an interaction between fields. Virtual means that an effect is described with it, but does not exist as a particle. Here, one must be satisfied with the observation that elementary charges with the same polarity repel each other without a field weakening occurring. And that elementary charges of opposite polarity (electron and proton) attract each other and emit photons in the process. (A new separation can be achieved by the action of photons).