Where is the UI menu option for "Separate by loose parts"? After APPLYing an array, P doesn't load it for me, rather in Object mode it brings up the "Set Parent To" menu, and in edit mode it brings up the "Make parent?" menu. I've tried to create my own hotkey using this function "bpy.ops.mesh.separate(type=loose)" or "bpy.ops.mesh.separate(loose)" but firstly, there's so many hotkeys I can't be sure whichever one I choose (Shift + 9) isn't being overridden by another one, and it won't show me any error if something isn't setup correctly either. Is there a UI or menu or button that can be accessed without hotkeys with "Separate by" options?

Preferred answer sequence:
1. Yes, the menu is here (no hotkey involved)...
2. You are doing it wrong. This is how...
3. Here is how to create your own hotkey to do it (that won't be overridden by another hotkey)...

Thanks guys!!
Make sure that you're presing P in edit mode, not object mode.
If that doesn't work you can find the separate action here (Mesh > Vertices > Separate > By loose parts):



You can check if the configuration is right on File > User Preferences > Input and search for "separate" and look on "mesh":