Little device that looks like a dish rack but with little spaces for pieces of bread! See image: https://www.google.com/search?q=toast+rack+regency&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiG5sHPvYnfAhXict8KHb8YA54Q_AUIECgD&biw=1309&bih=718#imgrc=_YlO5991b_YC7M:

"Bilious"= an excess of bile that comes from Hippocrates' theory of the four humours (melancholic, phlegmatic, sanguine, and choleric). http://www.oed.com/view/Entry/18971?redirectedFrom=bilious#eid

Arthur is talking himself into circles, seems to be anxiously repeating himself and oversharing.

Dull or expressionless

Vanity was a common theme in Persuasion, and since this was Austen's most recent work following the novel perhaps this was a significant characteristic on her mind...

Dramatic over exaggeration through repetition, seemingly satirical on Austen's part to poke fun at the characters.

Charlotte making a sassy comment that could risk coming off as a rude accusation to the host --> risks propriety.

Austen's use of Arthur as comedic relief. Although he says he is not afraid of much, he proceeds to list many aspects of nature that make him weary for his health even though his conversation with Charlotte is quite short. Perhaps a parallel with Mr. Collins of P&P? Awkward...

Moving behind Arthur so that Charlotte would feel less heat coming from the fireplace! http://www.oed.com/view/Entry/173439?rskey=TEeauT&result=1#eid

Each of the carriages, which were commonly used to carry mail, had space for 2/3 passengers -Encyclopedia Britannica https://www.britannica.com/technology/post-chaise