Austen reiterates the idea of gossip that is mistaken and misconstrued, and it is both relatively innocuous and sometimes effective to the plot by introducing conflict. For example, in Pride and Prejudice with the gossip over Mr. Bingley and who would join his party, the story of Mr. Darcy's treatment of Mr. Wickham, and then the suggested engagement between Darcy and Lizzy Bennett.

The definition of "mulatto" according to an American census in 1850 is a person who "has from 3/8th to 5/8th black blood." There were no instructions on how to determine the percentage of African ancestry, besides the use of previous censuses and even skin colour. The British and later Americans with Caucasian ancestry were very particular in describing how much African ancestry a person had, which lead to specific rules and regulations on their behaviour.

Miss Lambe is the first and only person mentioned in Austen's works identified as other than white, and it is interesting that she is rich and the "most important and precious".

https://scholar.harvard.edu/jlhochschild/publications/racial-reorganization-and-united-states-census-1850-1930-mulattoes-half-br

The Miss Beauforts seem similar to Miss Crawford in Mansfield Park and Miss Isabella Thorpe in Northanger Abbey who were preoccupied with making an advantageous marriage by "capturing" or "captivating" a wealthy man.

This phrase is often used in Austen's works, referring to the particular society or selected families a person interacts with, and which usually indicates a level of social class. In Pride and Prejudice, Mrs. Gardener says she "moved in different circles" from the Darcys, and in Emma, Mrs. Elton hopes to install Miss Fairfax as a governess in a better circle than she might be able to procure on her own.

Mr. Arthur Parker seems interested in the Miss Beauforts as earlier he thought a short walk to Trafalgar to be a lot of exercise, but he is willing to do a bit more to see the ladies. He is one of several single men in Sanditon and he is likely a contender to be a part of a marriage plot. This is assuming that, like all of Austen's other novels, Sanditon contains a marriage plot.

The question is why Charlotte should view the meeting between Sir Edward and Miss Clara Brereton as bad for the latter. Is it because Charlotte already formed an unfavourable opinion of Sir Edward as being a lover of Miss Clara's while talking "nonsense" to Charlotte in order to annoy Clara and appear an admirer of hers too? Charlotte finds Sir Edward tiring and may think he is, despite his title, beneath Clara. However, Charlotte does note that Clara's poverty makes her acceptance of Sir Edward's attentions more understandable. If so, then Austen is acknowledging the need for women to consider economic benefits to marriage, while also possibly giving her support to the idea of love in marriage.

The assizes were criminal courts of more serious cases, presided over by a judge.

http://www.nationalarchives.gov.uk/help-with-your-research/research-guides/criminal-trials-assize-courts-1559-1971/

Chapter # 12 Synopsis:

Charlotte Heywood, Mrs. Parker, and one of Mrs. Parker's children, Mary, go to visit the Sanditon House of Lady Denham. Miss Diana Parker attempts to have Mrs. Parker request money from Lady Denham, but Mr. Parker prevents this by retracting his own single monetary request. On the way to the house, they meet Mr. Sidney Parker. He is Mr. Parker's brother and he will be staying at the hotel for a few days. He is 27 or 28 years old, attractive, fashionable, and lively. At the Denham House, Charlotte spies Miss Clara Brereton sitting and talking with Sir Edward Denham in a secretive, unchaperoned spot, which leads Charlotte to think badly of Clara.

See Austenprose for more: https://austenprose.com/sanditon-plot-summary-by-chapter/sanditon-plot-summary-chapters-9-12/

Miss Diana Parker's request to ask Lady Denham for money for various people that she does not know from a woman she likely does not know very well seems very impolite. Also, considering how little Lady Denham likes to part with her money, Diana's comments would be particularly provoking.

The West Indies were Caribbean islands where many of the British migrated to, mostly in the 16th and 17th centuries. These "West Indians" may be returning British citizens who had lived in the Caribbean.

https://genealogical.com/2018/06/11/british-migration-to-the-west-indies-before-1800/