Use external python libraries on Pyramid
Yes, all of those frameworks are simply running Python code to handle requests. Within limits you can use external libraries just fine.
The limits usually are dictated by the WSGI server and the nature of HTTP requests; if your library changes the event model (like gevents) or relies heavily on changing the interpreter state (global state, localization) or takes a long,long time to produce results, then you may need to do more work to integrate.
Can I use any external libraries that are developed for python on Pyramid?
I mean is it the 'normal python' to which I can import external libraries as I do with the standard python downloaded from python.org
What is the situation for Django and Flask and Bottle?
My intention  is to create backend for a mobile app. I want to do it specifically in Python because I need to learn python.
The app is a native android app. Therefore the there is no need to use response with nice html code. 
I just want Django/Flask/Pyramid to direct http request to relevant python functions. Everything else including user auth, database is handled by my code I write. Is there a better more simpler way to map http request/responses with the relevant functions without using these 3 platforms?
In case I use one of these can I still use my own libraries?