How many assistant professor or postdoc jobs do people usually apply for in mathematics?
1) Unless you have something close to an Annals level paper, I would say you should be applying for close to 100.  This probably isn't actually possible; to hit this number reasonably, you have to apply for temporary positions and for non-research oriented positions.  Think of it this way.  Positions taking applications on Mathjobs are getting something like 500 applicants.  You're probably more qualified than most applicants, but if you're in the top 100, and a position hires uniformly at random from the top 100, then you need to apply to 100 to have expected value of one job.

2) Most recommenders are willing - they're blaming the university for not taking Mathjobs applications, not you.  If you want to save your recommenders trouble at the expense of your money, you can use Interfolio, which is a company that sends out applications - including confidential letters - for you.