Mathematica usage (success stories) for financial back-ends

Here are a few pointers. For question 1 you can find information, for example here and here. There are some user stories on that page. Other companies/products in that area (and there are many more) are for example UnRisk or RapidBusinessModeling.

Concerning point 2, yes unit testing is available via Wolfram Workbench UnitTesting. In fact most of Mathematica's unit tests are done with this. To run unit tests outside of Workbench have a look here.

Concerning point 3, a large extend of Mathematica is written in Mathematica. More that 1MLOC can be managed with WolframWorkbench, no sweat. Concerning organization, a Mathematica Package is a unit which collects functionality in it's own context (name space).

For your first question you can look at the customer stories in finance and analytics.

You might also be interested in the recordings from the Wolfram Finance Platform virtual workshop.

The question is a little broad. In my shop, we routinely use Mathematica for risk analysis and portfolio reporting, also for hypothesis testing and a variety of other front-office tasks. We have a master library of functions that we have created for these purposes over the last six years or so, and we also created the MathematicaLinkToBloomberg package that is (as of 2016) available at Github and elsewhere.