If you paint a picture of a character from a book

It really comes down to the purpose (relevant law):

for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright

As well as the following characteristics:

1. the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
2. the nature of the copyrighted work;
3. the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
4. the effect of the use upon the potential market for or value of the copyrighted work.

Painting a picture could very well fall under 3 (renders from descriptions in a book probably aren't "substantial") and 4 (a painting of a description is unlikely to diminish the original work). That said, if paintings already exist and yours looks substantially similar to those, it could violate the copyright of those paintings.

Fan fiction, however, directly competes w/ the original work and borrows more directly from existing works, so it would come down to how much it borrows. Writing something in the world of a book may be fine, whereas including specific characters from that world may not. It all comes down to the intended purpose and the characteristics listed above, as well as how well you can argue your case.

And yet in the eyes of the law Disney has every right to stop you since they might decide to start up a tombstone business next week.

I don't think that's true. I'm guessing what happened is that Disney threatened a lawsuit and the father didn't want to fight it, even if he had a strong case. That said, I don't know UK law and how it relates to US patents, so maybe Disney has a stronger case there than they would in the US.

But yes, I agree with the general point here: be very careful with copyrighted works, especially if a big, litigious company owns it (e.g. Disney).

It's also only actually parody if you are using the material to make a commentary on the original work.

Someone like Weird Al gets explicit permission for all his works. (Though the extent that that's respect for the artists vs legal necessity may be debatable because he does tend to comment on the work he's imitating.)