There are many different types of fields such as electron field, magnetic field, higgs field, electric field, quarks field etc, my question is do these fields interact directly with each other? Particle can form when the field becomes excited and different particles may interact with each other directly. Electric field and magnetic field are interacting with one another to become photon right? Or photon is the excitation of electromagnetic field which is a standalone field from others?
You are mixing up two different types of field.
The electron, Higgs and quark fields are quantum fields. The excitations of these fields appear as (real) particles.
The electric and magnetic fields are different aspects of the electromagnetic field, and this is a gauge field. It describes the interaction between charged particles as the exchange of virtual photons. Gauge fields don't have fundamental excitations with corresponding particles.
Quantum fields can interact and exchange energy and momentum with each other, and the possible ways they can interact are described by the Standard Model. Gauge fields are not fundamental objects and any interaction is described by interactions of the quantum fields that mediate the gauge force.