I have to find out which feature is identified on the map, thus subsequently read the attributes of the feature, and then do some logic to plot a time series graph. Is it possible to find out which feature is identified on the map using the identify tool, or alternatively is it possible to find a graphic below a mouse click using python in ArcGIS.
Short answer: No.
Long answer: Access to the user interface from python (ArcPy) is very restricted. You generally can do less in ArcPy than e.g. in the .NET interface of ArcObjects. But it seems that even in AO that task is impossible. The Identify tool doesn't seem to have any interface to access the objects which are currently displayed. Ergo, it is impossible to do what you ask for.
 What you CAN do is to program a new tool, add it to a toolbar, click on one of your desired features and execute your other code from that command.