In a Django web application, would large files or many unnecessary import statements slow down my server?
No, code speed is not affected by the size of your modules.
Additional imports only affect the memory footprint (a little more memory is needed to hold the extra code objects) and startup speed (more files are loaded from disk when your Django server starts).
However, this doesn't really affect code running speeds; Python does not have to do extra work to run your code.
In my Django web app, I have pretty much one large file that contains all my views.  This has a ton of imported python libraries that are only used for certain views.  
Does this slow my code?  Like in python does importing things like python natural language toolkit (nlkt) and threading libraries slow down the code when its not needed?
I know its not great for a maintainability/style standpoint to have one big file like this, but I am asking purely from a performance standpoint.