I would build this application in 4 layers:
1. The database: Contains all the data pulled from the api so far
2. The data pull: Pulls data from the twitter api. This can be a cron job, a simple "pull for every client request", or a combination thereof.
3. The backend: The root directory serves the frontend, while a /api-directory serves a "simple" CRUD application, serving the twitter data from *our* database to the frontend, and possible also triggers a data pull from 2.
4. The Frontend: Graphs, graphs and graphs: This will either pull data from *our* database, or from the twitter api (I would prefer our database, easier to avoid throttling from twitter that way).
Of course, if you have a better way to build this, I'd be all ears!
Regarding payment: I'd say a milestone payment for each module, or 50% in case there's no modularity.
Regarding time: Approx. 2.5 days per module plus 2 days for testing and general quality control, or 12 days in total.
Also, when you respond to this bid, could you kindly attach the screengrab you wrote about in the project description?
Hope to hear from you soon,
Marcus