I need more insight about the satirical aspects of the topics that are mocked in The Importance of Being Earnest ?
The best way to address your question is to establish the reason why Wilde chooses to mock and satirize important topics such as marriage, courtship, honesty, financial stability, and the commitment to family in his most famous play The Importance of Being Earnest.
There are a number of reasons. First, the complete name of the play says that it is a Trivial Comedy for Serious People. That, alone, is a giveaway that the play is meant to push buttons and perhaps even aggravate the common Victorian folk, which is made of prudish, hypocritical and high-minded people. Wilde especially detested that aspect of the world in which he lived, and this is why he devoted his talent and genius to making sure that he mocked and satirized them.
Secondly, during Wilde's time the institution of marriage was a laughable affair because, whereas women would vow for eternal love and commitment to their husbands, we clearly see how Gwendolen and Cecily also do this: As long as their husbands' names are Ernest. This is a direct hit to Victorian marriage because even Lady Bracknell makes it obvious that marriage is nothing but a social convention aimed to accelerate your social standing and financial stability. Marrying well is so important that even the family name matters, this is why Lady Bracknell, upon knowing that Jack is found in a handbag and can't claim any family name, says:
You can hardly imagine that I and Lord Bracknell would dream of allowing our only daughter—a girl brought up with the utmost care—to marry into a cloakroom, and form an alliance with a parcel?
Wilde equally satirizes honesty and commitment in the characters of Jack and Algy, who are men that should be fulfilling the duties of gentlemen. However, they both lead double lives in order to avoid these responsibilities and, moreover, they use these double lives for their personal needs for mischief. Jack does not like to pay his dining bills and uses his "Ernest" alter ego to eat at expensive restaurants and never pay. Algernon uses his fake sick friend Bunbury to break with family commitments and do as he likes. Both men fail the expected behaviors of the Victorian gentlemen: Their behavior shows the contempt that Wilde feels for the so-called "good man" of his time.
In the end, the importance of truth is satirized when we find out that Jack and Algy are the sons of the same man and that the man's name is Ernest. Duly, they are also "Ernests" and therefore their lies have become true. Nobody will suffer any consequence for deception. In not so many words: It is OK to lie, after all.
Therefore, Wilde takes every aspect that Victorians used to brag about: Their "goodness", their dignity, and their decency and exposes the hidden aspects of the so-called "upper and better classes" to mock them as much as he wants.