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Answer:
This question was kindly answered by Dr I.

The reason why oil can be dissolved in water when a surfactant is added
  First of all, think about the reason without considering the decrease of interfacial tension. Of course there is a relationship between them, however, it is micelle formation rather than the decreasing of interfacial tension that plays an important role in dissolving oil in water.

  Surfactants form an aggregate, called a micelle in the aqueous phase when their concentration is increased. This aggregate is spherical, the hydrophobic part （carbon chain） of the surfactant turns toward the inside, and the hydrophilic part is turned toward outside. Therefore, oil can easily go inside the micelle. This phenomenon is called “the solubilization of oil by micelles”.

Interfacial tension
  Interfacial tension is a force at the interface that acts to decrease the area of the interface. Actually it is possible to measure the interfacial tension. A drop of water can hang down from the edge of a glass tube using the force at the interface. However, when the interfacial tension is weaker, only a smaller （lighter） drop can hang down from the edge of the glass. The interfacial tension can be measured using this phenomenon.

The reason why surface tension is decreased when something is adsorbed on the surface
  The attractive force between water molecules is greater than that between other molecules because of the hydrogen bonding. At the surface, the attractive force works only from inside since there is no water on the outside （air side）, so a water molecule on the surface is strongly attracted toward the inside. This force is called “surface tension”. However, when something is adsorbed on the water surface, interactions between the adsorbed molecules themselves and also the adsorbed molecules and the water occur at the surface, so that the surface tension decreases.


Acknowledgement
  We would like to thank Dr. I for his careful teaching and kind support for this answer.