How to change vertex color and vertex size at the same time of Graph

This input

HighlightGraph[GridGraph[{3, 3}], {1, 2}, VertexSize -> .2,Style[{1, 2}, Blue]]

is not valid syntax for HighlightGraph. VertexSize is an Option and so it must come after all the other arguments

HighlightGraph[GridGraph[{3, 3}], Style[{1, 2}, Blue], 
 VertexSize -> .2]

Just for fun, here is another way you can modify properties of vertices and edges:

g = GridGraph[{3, 3}];
AnnotationValue[{g, {1, 2}}, VertexSize] = .2;
AnnotationValue[{g, {1, 2}}, VertexStyle] = Blue;
g

You can specify VertexStyle directives using Style and

1. use the form {Alternatives@@vlist1 -> optionvalue1, ...} for setting the values of other Vertex* options:

HighlightGraph[GridGraph[{3, 3}], 
  {Style[PathGraph[{3, 2, 1, 4, 7, 8, 9, 6, 5}], Red, Thickness[0.01]], 
  Style[{3, 5}, Green, EdgeForm[{Purple, Opacity[1], Thickness[.02]}]]}, 
 VertexSize -> {3 | 5 -> .2, 1 -> .3},
 VertexShapeFunction -> {3 | 5 -> "Square", 1 -> "ConcaveHexagon"}, 
 VertexLabels -> {3 | 5 -> Placed["Name", Center]},
 VertexLabelStyle -> 16]

2. or use Property[vlist, {options}] (Annotation[vlist, {options}] in version 12.1+) to specify Vertex* options for vlist:

HighlightGraph[GridGraph[{3, 3}], 
 {Style[PathGraph[{3, 2, 1, 4, 7, 8, 9, 6, 5}], Red, Thickness[0.01]], 
  Property[Style[{3, 5}, Green, EdgeForm[{Opacity[1], Blue, Thickness[.02]}]], 
   {VertexSize -> 0.2, VertexLabels -> Placed["Name", Center], 
    VertexShapeFunction -> "Hexagon"}]}]