How can I access the properties of an image?

The rules you mention can be extracted using Options. Note that this does not find all properties, e.g. the image dimensions are not explicitly stored in the Image.

Example:

In[1]:= Options@ExampleData[{"TestImage", "Lena"}]
Out[1]= {ColorSpace -> "RGB", Interleaving -> True, 
 MetaInformation -> <|"Comments" -> <|"Software" -> 
      "Wolfram Mathematica 8.0", 
     "Creation Time" -> 
      DateObject[{2010, 2, 18, 12, 43, 31.}, "Instant", "Gregorian", 
       2.]|>|>}

Some information is stored in options:

Import["path/to/file.png", "Options"]

{"BitDepth" -> 8, "ColorSpace" -> RGBColor, "ImageSize" -> {419, 348}}

More information is available by using "Rules":

Import["path/to/file.png", "Rules"]

This is only for use with images stored on your computer. It is not for images that have already been loaded into Mathematica. (To get data from already imported images, use Mathe 172's answer.)