I haven't looked that deeply into quantum physics so I may have some misconceptions but the way I always saw it is this:
The atoms of the resistive material do not allow electrons to flow easily (collisions). They flow easily through the wire then begin to pile up at the resistor. This sets up electric fields in the resistor. You will eventually reach a balance, where these piles of charge prevent others from piling up and 'guide' the others. In this balance there is no more piling up and things flow as fast as they can, against the electric field.
That electric field from the charges is the voltage drop. Voltage is created by electric field over a distance.
The interactions are electrons struggling against the electric fields of other electrons and from the battery. The movement against or with a force is the energy exchange.
The electric field's force set up by the charges in the resistors has to be equal to the battery's electric field's force because it's a reaction. The battery pushes until the electrons push back with equal force.
With more resistance the electrons have a harder time flowing so the charges pile up more before you reach a balance, giving you a larger voltage drop for a smaller flow.