When you finish the meshing process and to check its quality, you have to notice that the maximum value of the skewness is less than 0.85 and GCI is less than 0.05. 

You have to test the Grid Independence. If GCI ( Grid Convergence Index) less than 5%, you can say, the solution is grid independent. Richardsons method is the best one.

grid independence is the only way you can use for your simulations if you dont have any experience. 

Keep in mind that the mesh size should be smaller than the suspension portions (or particles or bubbles) in your simulation if you use VOF. Also you can you finer mesh if there is any interface between oil and water. 

generally, it depends on your problem and boundary conditions

hope it would be useful.

If your flow problem is laminar, there is not a great problem in the mesh size, you should get a cell Re number = O(1). But if you  have a transitional/turbulent flow the things are very different as you have first to decide the formulation to adopt (RANS/LES/DNS), each one having different requirements for the grid resolution.

 You need to conduct a mesh sensitivity analysis as Hamid and Panayampilly said. If you are interested in capturing the interface, considered at least 3-5 cells across the interface. 

for laminar flow, using do loop in FORTRAN or MATH LAP PROGRAMS

and if turbulent ,increased the number of cells in order to reduction the effets

ax=x/20.

ay=y/20

x and y are the dimensions of problem

20 is the number of cells and can be increased 

ax and ay are the dimensions of cell

  X(i) = (i-1)*ax

Y(j) = (j-1)*ay  

I would be very careful to use a grid independent search for this type of problem. Oil-water should be immiscible so the interface is a discontinuity surface, you should properly define the variable to check for independence.

When you finish the meshing process and to check its quality, you have to notice that the maximum value of the skewness is less than 0.85 and GCI is less than 0.05. 

If the problem is transient you might want to think carefully about the advice given. Because of Courant number considerations if you have too fine a mesh you will need to have very small time steps. For certain problems it can be better to have reasonable time steps and a coarser mesh.

In general there are good rules for what is the best mesh. In practice there are always compromises that need to be made. The most important thing about any simulation is what do you need to do to provide the answers to the questions which are driving the need for the simulation in the first place. Sometimes (rarely) it is the perfect fine hex mesh that is best to resolve LES, most of the time a quick and dirty tet mesh with appropriate inflation layers and enough sizing controls to resolve the geometry is enough/

Try fine meshing near wall and interface based on turbulence model chosen

Is it fundamental based or application based study?

Its depends on your problems and don't forget the computational time.

Do grid independent test . Refine the mesh near wall based on the turbulence model chosen