The different sizes are created by the unnecessary "GraphicsGrid" that scales the different pictures. Without it:

SimplifyShape := Rectangle[{0, 0}, {1, 1}, RoundingRadius -> 0.1]
exp1 = Table[{EdgeForm[Black], Hue[Sqrt[x]], 
    Translate[Rotate[SimplifyShape, x], {x*1.5, 0}]}, {x, 0, 10, 1}];
exp1 // Graphics

The different sizes are created by the unnecessary "GraphicsGrid" that scales the different pictures. Without it:

SimplifyShape := Rectangle[{0, 0}, {1, 1}, RoundingRadius -> 0.1]
exp1 = Table[{EdgeForm[Black], Hue[Sqrt[x]], 
    Translate[Rotate[SimplifyShape, x], {x*1.5, 0}]}, {x, 0, 10, 1}];
exp1 // Graphics

Update

If you want an "regular array", that is a vector, of images the same size, use RotateImage:

exp1 = Table[
   ImageRotate[
    Graphics[{EdgeForm[Black], Hue[Sqrt[x]], SimplifyShape}], x, 
    Background -> Transparent], {x, 0, 10, 1}];
exp1