Keen IO is an analytics backend as a service. We built it so that developers wouldn't have to build in-house analytics infrastructure ever again. You can use our SDKs to track any event in your mobile app, website, or backend, and we expose powerful analytics features by API so you can do whatever you need to do with your analytics data.

There's no easy drop-in solution that will give you all the answers for your specific business, but we tried to make our platform extensible so that it can be used answer any type of event-based analytics questions (like those mentioned here).

Plugging my own thing again, I built http://www.instahero.com to solve this exact problem. It has many pre-made metrics where you just select your inputs and it gives you the metrics on a dashboard/report.