There's a couple routes you could travel. The first, is ads. You mentioned the data is usable? Do you have an API for which to grab it with? If so you could charge for access to that. But it's hard to suggest options without knowing more about the business
You can do this by using a server backend such as Parse. They have a free SDK. There are other similar options and I believe apple is rolling out the same thing in iOS 8 with CloudKit.
There's no "reliable" way to do this, as you're interacting with one or more shippers. After shipping physical product around the world since... 2003... every shipper only gives ballpark windows of when they can complete a delivery. Using Amazon FBA will likely provide fastest delivery times.