All of these look very, very do-able with B4A.
For your storage/distribution/notification system, you will definitely need a server side component for your app to query/upload/download.
There are several examples of almost all of these items done individually in B4A, and should be able to get a prototype in place within a few days of coding if you are familiar with Basic style programming, or within a couple of weeks if you aren't . (to give yourself time getting used to B4A)
The most advanced topics would definitely be the server side/service modules (at least for me), but I've looked through several examples that look pretty straight forward to implement.
Ross