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What do I have to do if I want to invert the color scale in "AvocadoColors", and add a condition that the zero value is denoted as white, whereas rest of values (> 0) are shown accordingly to "AvocadoColors" scheme?

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ColorData[{"AvocadoColors", "Reversed"}][0]

RGBColor[1., 0.984375, 0.230411]

You can temporarily define this color as White using Block:

data = RandomReal[1, {50, 3}];
ldp1 = ListDensityPlot[data, ImageSize -> 300, 
   ColorFunction -> ColorData["AvocadoColors"]];
ldp2 = ListDensityPlot[data, ImageSize -> 300, 
   ColorFunction -> ColorData[{"AvocadoColors", "Reversed"}]];
ldp3 = Block[{RGBColor}, RGBColor[1., 0.984375, 0.230411] = White;
 ListDensityPlot[data, ImageSize -> 300, 
  ColorFunction -> ColorData[{"AvocadoColors", "Reversed"}]]];

Row[{ldp1, ldp2, ldp3}]

enter image description here

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A safer method than redefining a color would be to use Lighter[] with a sharp exponential or Gaussian drop, e.g.

DensityPlot[Sin[x + Sin[y]], {x, 0, 6}, {y, 0, 6}, 
            ColorFunction -> (Lighter[ColorData[{"AvocadoColors", "Reversed"}, #],
                                      Exp[-#^2/(1*^-3)]] &)]

avocado with white

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