mainframe_kdm

1) It depends on the business goals. In terms of cost, there are a bunch of studies, but basically, distributed is cheaper when you start out, but the costs of a distributed environment rise very quickly. z/OS is more expensive to set up a base environment, but the costs rise much more slowly as the workload grows.

2) Depends on the person. And sometimes, they're the same thing; you can look at something that looks like a very silly design choice, but then you look at the history behind it, and discover that 30 years ago, it made a great deal of sense.

5) Because I always enjoy showing this to people: IEFBR14

Analytics, certainly. With the newest mainframe, the z13, computationally intensive tasks can benefit greatly from SIMD. The data you're mining is usually there already, so that makes things much easier. And in general, z/OS/mainframes were the cloud before it became the buzzword. So anything where the data and processing is done elsewhere, and then the results are the accessed on a different device, can certainly be done on z/OS.

There are also the Master the Mainframe contest and some schools also offer access to z/OS images running under z/VM.

These days, Matrix references are a bit more prevalent internally. It's age dependent, I suspect.

Python, at least, is available from Rocket Software.