Firstly, as I understand it, the Strategy & Operations practice is different from the Finance practice (which deals with improving the finance function across various industries). The careers ad appears to combine the two in the title (perhaps to make it more attractive), but the description is more finance transformation.
In response to your questions
1. They are not looking for an auditor, in fact quite the opposite. They are looking for someone with a good understanding of the finance function with experience of doing project work, designing solutions across process, technology and implementing change.
2. Being in the UK, I'm not that familiar with the requirement for MBAs. I can say
- the big 4 are unlikely to require a top ten school
- they have an intake route at senior consultant level for MBAs (with no prior consulting experience)
- new graduates are expected to do an MBA after a couple of years before returning.
3. Network - I'd suggest speaking with someone from your current firm, preferably someone who works mainly in financial services (regardless of whether they do strategy, ops or finance transformation) as I think this could be your best route in. FSI clients are always doing some form of transformation, find out where they feel your skills could best support.