Charlotte is surprised that Lady Denham's objections to having more people stay at her home are not based in her affection and duty toward Miss Clara, but because she doesn't want to pay her housemaids for doing the extra work involved.

An estate settled on a wife for the period during which she survives her husband, in lien of a dower.

https://en.oxforddictionaries.com/definition/jointure

A widow with a title or property derived from her late husband.

https://en.oxforddictionaries.com/definition/dowager

Flashes or sparkles.

This presumably is in reference to Robert Burns's well known love affairs. See section "The Life of a Lover and Writer": https://www.biography.com/people/robert-burns-9232194

This is from Scott's "Lady of the Lake," and Sir Edward Denham seems to quickly forget the rest of the lines.

Here is a synopsis of "Lady of the Lake" and link to full work: http://www.walterscott.lib.ed.ac.uk/works/poetry/lady.html

These lines are from Sir Walter Scott's "Marmion."

"O woman! In our hours of ease Uncertain, coy, and hard to please, And variable as the shade By the light, quivering aspen made; When pain and anguish wring the brow, A ministering angel thou!"

This is not the greatest description of women, and Austen seems pointed in how she uses Scott's work.

The full poem: https://archive.org/stream/marmion05077gut/marmn10a.txt

This may imply that despite having other published work at the time, "Lady of the Lake" and "Marmion," quoted below, were the most popular/wide read.

Lady of the Lake: https://www.gutenberg.org/files/3011/3011-h/3011-h.htm

Marmion: https://www.gutenberg.org/files/4010/4010-h/4010-h.htm

Austen is referring to the Romanticism poetry of Sir Walter Scott, a popular poet and novelist at the time.

Biography of Scott for context: https://www.britannica.com/biography/Sir-Walter-Scott-1st-Baronet See particularly his "literary gifts," interest in German Romanticism, and ambiguity of his feelings towards Scotland.

The era of romanticism is marked by a preoccupation with the sublime, or of awe inspiring, overwhelming beauty, and a return to nature. Romanticism focused on large emotions, and its writers sought to capture and recreate art in a visceral way, approaching the sublime, focused on nature and natural imagery.

Miss Denham is jealous of nicer vehicles, as a gig is a lightweight, two-wheeled cart:

"The gig was more formal than a village cart but less formal than other carriages or coaches. It also had a somewhat cheap reputation having received its name from a contraction of “whirligig,” because similar to the whirligig, the gig whirled rapidly. (https://www.geriwalton.com/the-gig-or-chaise/)