Dedicated web service for web app (Python/Django)
By creating dedicated API's will help you in future if you decide to build mobile application, that case no need to write new API's as you can consume your existing API's. By doing this your are not repeating your server side codes. Only have to write the client side code. And coming to performance only load time will be more as it has to load HTML, JS and CSS after subsequent requests will be more faster
Let's assume that I want to create a simple todo list web application. I am thinking about creating RESTful web services which will be used my the web application and which will be providing all functionalities concerning managing todo list and tasks. I have two concerns:

Is there a sense in creating dedicated web service assuming web service will be only used by my web application? Web service and web application will be on the same server and there have to be a lot of 'views' duplication. Web application will only delegate request to web service, process the response, and return a web page.
Assuming I decided for this kind of architecture: dedicated web service + web application, what is the best practice for calling web service from views in web application? They will be just two different apps within Django project. request?