Every now and then I see one of these, and I think of how long I spent trying to purge COBOL from my resume. It boggles the mind. I'll try and answer the questions in order.
1) It's very hard to get one of these jobs, because the paradigm is so outdated. There are no new systems (effectively), so you're competing against people who've been doing it forever. Fortunately a lot of them are dying, so occasional positions do open up.
If you get one of those positions, prepare to be hated. HATED. Because this stuff is so old, you're going to be dealing with incredibly hard to maintain code. Tons of customization. Very old development models. The learning curve is steep, and you will not be as responsive as the person who just retired/died. You will spend years trying to overcome this.
2) A lot of this stuff is financial code, and financial code has to change to reflect changes in the law. Changes in tax law will keep you in new code forever.
3) Step 1, get a mainframe. No, seriously, there is practically no way to learn. Fortunately, most companies don't really expect you to have experience. They just want it if they can get it (which they probably can't). If you're dealing with a "standard" OS, you may be able to get some classes (HP-UX, AIX, etc). Most of the mainframes still in production will probably be using much older versions of those, however, and you won't be able to get classes. God forbid you find a job where the mainframe is running something really bizarre (MPE/iX leaps to mind). There are barely even books for that.
4) Absolutely not. Your job is to talk to the accountants and make their math into code. You shouldn't ever be doing your own math. The auditing requirements on the code are unbelievable...Prepare to have to justify every change you make to every program you touch. Spend an hour trying to understand a piece of code, and then feel the desire to add a helpful comment? KILL IT. Every change has to be extensively documented.
I don't know. I sort of fell into this (Y2K got me COBOL experience), and I've been fighting it ever since. It's no fun. You're always working on systems that everyone hates, systems that have been slated for replacement for decades. Nothing is ever new or fast or easy.