Django as a service login and logout
I don't think so. If this is safe for using on web pages, why should it be a problem for API calls?
If you are really worried about someone getting session IDs, use SSL to encrypt your communication. But that should be the same for web resources as well, you should use https if you don't want session cookies to be stolen.
I have a rest API in Django 1.6 but I'm not using any library like django-tastypie or other to do that. I just write my endpoints (urls.py) and return json data in my views.py. For authentication I'm using django basic auth provided. So in every request made by front-end I check request.user.id and with that work to know if that user has access to a certain resource in other words I'm using login session data that django puts when front-end calls login endpoint. Am I incurring safety issues doing this?