Dickens makes an allusion employing a parody of the stereotypical English churchman in Chapter 4, when Pip describes how the officious Mr. Wopsle says grace at his family's table:
It began the moment we sat down to dinner. Mr. Wopsle said grace with theatrical declamation — as it now appears to me, something like a religious cross of the Ghost in Hamlet with Richard the Third — and ended with the very proper aspiration that we might be truly grateful.
When characters act pompously in a Dickens novel, the author is most often indicating that they shouldn't be taken seriously by the reader. Mr. Wopsle is a parody of the self-important Victorian clergyman, who takes his own voice so seriously that he later moves to London to become an actor. The officiousness and silliness of Mr. Wopsle shows in his hyperbolic "theatrical declamation" of a simple mealtime prayer with friends. This is a strange occasion to speak in "theatrical" tones, but no one except Pip seems to blink an eye at either its delivery or "aspirations."
The "Ghost in Hamlet" and "Richard the Third" that Dickens alludes to are characters in plays by William Shakespeare. Both are kings, both are known for ominous and dramatic speeches, and both are very long-winded. It's also notable that Mr. Wopsle's silly "grace" drags on, and Richard III and Hamlet are the two longest plays that Shakespeare wrote. Pip, in his position as first-person narrator, remembers this incident with tongue-in-cheek humor, describing it in a way that his childhood self, unaware of the finer points of Shakespeare, wouldn't have understood at the time.
Although Miss Havisham herself is already quite ghoulish company, Dickens employs one of his most corrosive satires to describe her unpleasant and sycophantic family members. When Pip visits Miss Havisham in Chapter 11, he immediately dislikes her relatives, implying that they are disingenuous and false:
There were three ladies in the room and one gentleman. Before I had been standing at the window five minutes, they somehow conveyed to me that they were all toadies and humbugs, but that each of them pretended not to know that the others were toadies and humbugs: because the admission that he or she did know it, would have made him or her out to be a toady and humbug.
A "toady" is the Victorian equivalent of a yes-man, and a humbug is someone who speaks deceptively or falsely for their own benefit. The people Pip sees in the room are, sadly, Miss Havisham's only remaining family: Sarah Pocket, Camilla, Georgina, and Raymond. Havisham is certainly nasty, but she at least presents her nastiness honestly. The same cannot be said for the visitors who throng around her attempting to win her good graces. Currying favor like this is a trope in many Victorian realist novels where money is a central concern.
These people are all entirely self-serving, like many of the frivolous minor characters in Great Expectations. They are also almost totally un-self-aware, as they "pretend not to know" that they are all "toadies and humbugs" in order to preserve their delicate self-images. Havisham's family thrives on gossip and intrigue, and they are only interested in the old woman for the money they believe she will leave behind. They all protest about which of them cares for her more, protests which, the narrator indicates to the reader, are completely untrue. Each of them seems to know this about the others. They take turns jabbing at each other's attempts to be sympathetic in some very funny exchanges of cruel one-liners. At one point, Raymond makes fun of Camilla for the "nervous jerkings" she says are a result of caring too much for others:
Camilla, my dear, it is well known that your family feelings are gradually undermining you to the extent of making one of your legs shorter than the other.
The ridiculous image of hysteria shortening one leg is an example of hyperbole. Of course, this is just Dickens making fun of Camilla's hysterical excesses, as the crew work themselves up into a frenzy. This all seems quite pointless in the end, however, as Miss Havisham herself does not buy their sickly-sweet comments. She knows they are there to try and get things from her, and accuses them in the same passage of wanting to "feast on her" after she dies.
Miss Havisham is a particularly selfish, dramatic, and intense character, and Dickens often uses hyperbole to make her self-importance and love of melodrama apparent to his readers. In Chapter 11, Pip doesn't satisfactorily press her to explain why she hates her birthday when she brings it up. Annoyed, and poking flamboyantly at the cobwebs on a decorated table, she utters the following hyperbolic monologue:
“On this day of the year, long before you were born, this heap of decay [...] was brought here. It and I have worn away together. The mice have gnawed at it, and sharper teeth than teeth of mice have gnawed at me." [...] "When the ruin is complete,” said she, with a ghastly look, “and when they lay me dead, in my bride’s dress on the bride’s table—which shall be done, and which will be the finished curse upon him—so much the better if it is done on this day!”
Havisham's speech is so melodramatic and distraught that it cannot be taken seriously, as she compares her unhappiness to being nibbled by rodents. Remember, this is an old woman speaking to a young child who's been compelled to come and spend time with her in her own strange and creepy house. In this context, the "ghastly" look she gives Pip is funny, rather than scary, as she is something of a ridiculous figure.
The "completion" of the ruin she refers to is her own death, which she envisions as being exactly like her mausoleum of a life. She says, in so many words, that she hopes she dies on her birthday so her ex-lover is cursed. This is so spiteful it's also funny, but she means it seriously. Pip is alarmed by this as a child: he has no idea how to react to this clearly insane diatribe. In his role as narrator he says that he has "an alarming fancy" that he and Estella have begun to decay themselves because of the atmosphere in the house.