PHP Driven Web App

We are working on a project that will require heavy PHP development utilizing MongoDB as the backend database. Developer will want to

1) Create registration system using Facebook and Google API Connections;

2) Integrate an already coded front-end layout (its responsive design, HTML/JS/CSS sliced);

3) Animate one part of the front-end display;

4) Create an AJAX powered interface for data entry;

5) Be able to create complicated queries utilizing Mongo;

6) Be able to integrate complex data sets and mathematical calculations into the front-end;

7) Create an administrative portal to manage content.

Ideally we do like to see examples where you have actually done all these things.

Desired Skills are Facebook Development, AJAX, jQuery, PHP5, MongoDB