Use Blender game engine with bpy, is it possible? I am new to blender, I want to use bge with bpy as normal scripting. I intend to use scene graph and actuators also mouse events and stuff like these from bge, however importing bge into my standard file does not work. Can I write an operator that uses features from bge, or that is not possible?
No the bge module is only available when the game engine is running. Similarly, the sensors and actuators that you setup with logic bricks will also only work in the game engine.

To write an operator that responds to events you want to look at a modal operator. You can also find a few examples in the script template files that are available in blender's text editor.