AC transformers work only when an alternating current flows through the primary so as to induce current in the secondary.
Yes. Although we would be more correct in saying 'induces a voltage in the secondary'. When a load is connected to the secondary, a current can flow.
So for all the different transformers located in different areas leading right up to our homes, their must be an AC current flowing through them at all times right? Does this also mean that there is AC current continuously present in the distribution lines at all instants?
Yes. Even if there are no end loads being supplied, the transformers need magnetising current, and the lines need a charging current.
Also, is the return path for these AC currents through the transformers, be one of the phases of the three phase power lines thereby not needing an earth ground?
Yes. Although most of the distribution is 3 phase, so all three conductors are used. It would be a mistake to think that one conductor was the 'return'.
A slight caveat, a neutral may be created in a delta-to-star transformer, and then this neutral can be used as a return for the current, for some light single phase loads. However, it's more usual to supply single phase loads from a transformer fed from two phases.
Earth ground is never (knowingly) used for a supply return conductor. It is only for safety duty during faults.