When I load an Image as background in the viewport or in the camera. Is there any way I can check the properties such as its resolution etc from inside Houdini ?

I dont think it's directly possible through the camera or viewport. But you can provide a cop network as an image reference for the background of the camera or viewport. Then read the resolution in cops in the node info of the file.

To calculate the corresponding aspect ratios for the cam you can use vex [www.sidefx.com] or python [www.sidefx.com].