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Now I have a set of 3d discrete points in the form of {x,y,z} and want to interpolate them and define them into a function making x and y as the variables. Subsequently read corresponding values of z with x and y values which don´t exist in my data set. How to achieve this?

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Interpolation. If

list = {x1, y1, z1}, {x2, y2, z2}, .....}

then

func = Interpolation[ list ];

will give an interpolating function. Then you can get values by entering func[x, y] you will get the corresponding z. If these values are far outside the range of the input values, then the result will not be so reliable.

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