I am not sure I can help you so much as you expect.
For your system requirement, I have some ideas to share:
+ There are two parts you need to develop: Web portal and Mobile App. And both of them must be interacted together absolutely.
+ With web portal module, you can use some opensource PHP ( Drupal
],...) or Java-based such as Spring
] or just use JSP/Servlet....
+ With Android application, I recommend you should you PhoneGap
]. With this framework, you can build cross-platform such as : Android, Blackberry, Window Phone...
+ For the interation between Mobile App and Web portal, you can achieve by this way: at WebPortal, define some web serivces, then at Mobile, you will invoke via these web services. To invoke web service from Android application, you can use open source library ksoap2
], or you can use JSON