If it becomes public that she is in process of writing a new novel, will that mean that any of the options are correct? Even if she has no publishing deal arranged prior to it being done? Does she have to make a formal announcement or is the media reporting her telling someone else about a novel or other fiction or non-fiction sufficient?

A formal announcement would be best. Media reports can be misleading.

I will wait until an announcement, if any, is made on her official website.
ttp://www.jkrowling.com/

“Tales of Beedle the Bard”

Fairy tales from the “world of Harry Potter” with one copy previously sold for charity but now being widely published for release in December. 128 page book.

http://search.barnesandnoble.com/The-Tales-of-Beedle-the-Bard/J-K-Rowling/e/9780545128285/?itm=1#TABS

By the way, I’m thinking “Other fiction” since though it is “from Harry Potter’s world”, it is clearly not a novel (thus, not a “prequel novel” by definition) but a collection of fairy tales which seeming fits better into the “other fiction” category which includes “children’s bedtime book…or anything else shorter than a novel.”