Build my own navigation system [on hold]

I'm sorry but I don't know where to ask this question.

I have to develop a navigation program in my artificial intelligence course. To do it, I need a city map. Probably Barcelona.

I don't which is the format of a map used in navigation systems like Tom Tom or Google maps, but if I want to use graphs, the format could be georeferenced street corners.

Ok. My questions are:

1. 
   

   Where could I find city streets data to calculate a route between two locations?
   
   I have find it here http://ift.tt/1pIioqC.

   
   


2. 
   

   How do you could such kind of maps?
   
   Street network data.

   
   

And the last question is:

I used http://geojson.io/ to show the roads (file barcelona_spain-roads.geojson) but it is a mess because These data do not correctly represent the streets.. Where can I find better quality data? Or maybe I have to do something