Is energy always transferred from the source to the object when positive work is done by the source on the object ?
Yes, but be careful. If something else simultaneously does an equal amount of negative work on the object, the net work on the object will be zero.
If so, what energy is transferred from the earth to a freely falling body ?
Gravitational potential energy of the earth/body system is transferred to the freely falling body. Gravity does positive work giving the object kinetic energy per the work energy theorem.
The potential energy is converted to kinetic energy in the process. But I see no transfer of energy between the earth and the body.
Energy transfer to the body comes from the gravitational potential energy of the earth/body system. It does not come from just the earth, but from the earth/body system. Neither the body alone nor the earth alone has gravitational potential energy. It is a property of the earth/body system.
And how does energy transfer takes place in case of negative work ?
In the case of negative work, the force is in the opposite direction as the displacement. The thing doing negative work takes energy away from the thing it does work on, as discussed in the next answer.
When a body is moved across a surface which has friction, the friction does negative work. Does it mean that a sort of energy transfer occurs between the surface (source) and the body (object) ? If so, how ?
Yes. When friction does negative work it takes energy away from the object it does work on. What makes friction interesting, however, is that it involves both energy transfer to the stationary surface upon which the body slides from the object, and energy transfer from the stationary surface to the object.
Consider what happens when you rub your hands together. Take one hand and hold it stationary. Then slide the other hand over the surface of the stationary hand. Both hands feel warm. The temperature, and thus internal microscopic kinetic energy of both hands increases. In the frame of reference of the "moving" hand, the "stationary" hand is moving, and vice-versa. In effect, each does friction work on the other.
If a moving body comes to a stop, part of the lost macroscopic kinetic energy of the body goes into the internal energy of the stationary surface increasing its temperature and thus its internal energy. But part of the lost macroscopic kinetic energy is converted into an increase in the internal energy of the object itself, as reflected by an increase in its temperature. If, after the transfer, the body can be isolated (prevented from transferring heat with its surroundings), that increase in internal energy will be retained.
In my mind at least, friction illustrates that when applying the work energy theorem one must account for changes in both macroscopic and microscopic kinetic energy (internal energy). The overall reduction in kinetic energy of the object is actually the loss of macroscopic kinetic energy minus the gain of microscopic kinetic energy of the object.
Hope this helps.