Google for information about smart objects. To put it it simply click on a background layer and click on convert to a smart object and duplicate the layer. Any changes via Transform will now be made with little or no loss of information and anything that is lost will not be visible in any way. I would use the Skew transform on that image and when you line everything up then possibly Scale or Crop. I would also use the grid overlay. You can set the size of the squares in preferences and the colour of the grid.
