at http://Trak.io we can definitely handle that data volume, all data analysis is done retroactively and in realtime.
Note: However we don't automatically track any events, as we found most people were collecting a ton of garbage event data that they would never use. So you'll need to setup the events to be tracked at the beginning of the integration.
We don't have iOS or Android SDK's, but a raw REST http API (and JS) but we'd be open to discussing what we could sort out to win your business ;)
A/B tests: date vs. date cohort segmentation, event vs. event cohort segmentation, property vs. property segmentation. And groupby (breakdown by) view.
Trends
Linear funnels are in progress, but again for an app this size let's talk about what we could do.
The main way we differentiate ourselves from Mixpanel (and similar) is that we're trying to go for as simple interface as possible. Essentially, if analytics tools or reports are complicated, they just wont get used. So we're sticking to a very design-led product which may or may not suit you, depending on what exactly you're looking for.
Email me on liam@trak.io if you want to chat further :)