] Have I passed the test?

You most certainly have! Well done. I have a computer programme to help me but you have presumeably graduated to JA genealogical status (able to do it in your head/on paper). Now, there is only one eensy weensy little spanner in the works that I deliberately didn't mention. People had a horrid habit of marrying their own relatives. Lady Caroline Brydges husband (who was James Henry Leigh's father)was ALSO JA's first cousin once removed. His name was James Leigh and his own wife was a cousin once removed!! This means JA was actually doubley related to James Henry Leigh. Anyway, fortunately it didn't matter because they would have just referred to each other as "cousin" anyway.

] But it must have been difficult even for the Austen family to keep track of their relations without explaining in detail or putting it on paper.

Anyone who was anyone did indeed have pieces of paper in their library explaining how they were linked to other illustrious families. I have actually seen the real-life collection of the Willoughby family, (who are the Lords Middleton) held at Nottingham University Library. Special genealogy clerks could be hired to draw these pegdigrees for you.

The Austens definitely had some of these pieces of paper because we know that both James and Henry had scholarships to St. John's college Oxford, on the strength of being "Founder's Kin". Their 7xGreat uncle, Thomas White, Lord Mayor of London in 1553, had founded St. John's college and left a provision that all of his kin could be educated there on a scholarship. Thomas White had died in 1567 so obviously he couldn't turn up and vouch for the two would-be-scholars in person. Apparenty there is a copy of the original pedigree that James presented in the St. John's archives. I'd love to see it but unfortunately I am a 17 hour plane-flight away. This explains how the Austen's could afford to send two sons to Oxford (not cheap).

And of course, like Sir Walter, most gentry upwards would also have a baronetage/peerage/landed gentry. JA's friend Mrs. Lefroy was born Anne Brydges who was a 10th cousin once removed of JA. Her father and her famous brother & nephew, the genealogically-inclined writers, Sir Samuel Egerton Brydges & son were presenting an infamous case claiming that they should inherit the estate of the Dukedom of Chandos (JA's Great, great Uncle James Brydges was Duke of Chandos and married Cassandra Willoughby) which had fallen into abeyance. The biggest scandal was that one of their lawyers/clerks intimated that they had surpressed some unfavourable genealogical evidence and their case was thrown out of the college of arms (like a sort of "court' for proving ancestry - I think very important as it governed inheritance rights). It was a giant scandal and a source of huge public shame.