> 1. Are there any other fields apart from programming...

The personalized feedback could be really good for learning math. You could develop an "async" model for learning, where the student works on a proof (on their own) and tutor checks in once in a while to give tips and add corrections.

Note for basic arithmetic and algebra, the computer could check the answers automatically, but for proofs and more advanced/subtle arguments, the tutor will serve as the "math compiler" checking the student's work. Here's the discussion where the notion of a "math compiler" came up https://news.ycombinator.com/item?id=11267877