These should be pretty big and open-ended questions, compared to individual research papers that are smaller in scope. It’s similar to how songwriters have lots of “hooks” stored and software engineers keep “code libraries” of useful bits of code.

How to get new ideas? Surprise is an important signal when you are generating ideas

Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, ‘How did he do it? He must be a genius!

How Thiago Forte describes them in his book:

The power of your favorite problems is that they tend to stay fairly consistent over time. The exact framing of each question may change, but even as we move between projects, jobs, relationships, and careers, our favorite problems tend to follow us across the years.