Best Python Web Framework for my API Server Needs
Depends on what stage you are at, I would suggest to develop 2 systems because the load to pull data from 3rd party and the load to handle the API would be different.  You can scale them into a different types of nodes if you want.
Django-Tastypie (https://github.com/toastdriven/django-tastypie) is not bad, it supports all JSON, XML and YAML.  Also you can add OAuth easily.  Though, Django itself maybe a bit heavy for your needs at this time.
I am working on developing two systems:  

A system that will constantly retrieve economic data from a 3rd party data feed and push it into a MySQL DB (using sqlalchemy)  
A server that will allow anyone to query the data in the db over a JSON AJAX API (similar to Yelp or Yahoo API for example)  

I have two main questions:  

Which Python framework should I use in 2)? Pyramid is my first choice, but if you strongly suggest against it or in favor of something else like Django or Pylons I am definitely wiling to consider it.  
Should I develop the two system separately? Or should 1) be a part of 2), running within the framework (using crontab or celery for example)?