1 Can't they just live on their Lotteria Italia windfall? Since it came after their formative years, I don't see a problem. If they were published authors of, say, crime novels, they might have a case for some tax deductions as well.

2 Dorothy L. Sayers made her heroine into a mystery writer, but she did make sure to draw some distinctions between her character's detective and her own detective. She was, of course, accused of inserting herself into her own series, but I'm not sure that was fair: in fact, it made a nice little contrast, to show the different methods people might bring to real-life crime solving if they had real forensic experience vs. if their interest had been strictly literary. There is always a huge level of artificiality in these books, even the "mean streets" variety.

3 Well, I can see three possible options, knowing nothing else about this book or the previous one. 1. They could be, not independently wealthy, but comfortably well off and not interested in getting richer. Perhaps they have an income from investments/trust fund/whatever, which affords them a reasonable standard of living, and they prefer leisure to wealth, as the economists say. 2. Investigating crimes is part of their job. The obvious ones for this (besides making them cops) are private investigator, reporter/writer, and lawyer. I am not a great mystery fan, but it is my impression that all of those have been done a lot. 3. They have jobs that are seasonal or intermittent. I was once told that beekeepers, for example, don't work five months of the year. (Don't quote me on that.) Or some sort of event planner type job, where you work insanely for three weeks, and then have three weeks before the next gig. Any sort of job where your time off comes in big blocks, not regular weekends. If you go this route, of course, you will need to educate yourself on how those jobs actually work. Good luck.