This is one of Author Austen's lesser openings, in my opinion. By the time the story PROPERLY starts, after all this exposition, three of the people in the beginning have died, two of them without Christian names assigned them!
However, this prosaic little sketch that sets up the problems and relationships of the novel has Austenesque touches that leap out. The third paragraph notes the 'universal truth' that most wills give as much disappointment as pleasure. It also notes that the charm of a certain-age child is by no means rare, no matter what those relatives charmed by the child might think.
There are also points of human nature that Author Austen does not accent, but which make the story 'ring true' for me. Like: when someone has money to leave in a will, they are more likely to leave it to someone who already HAS money, not to someone who NEEDS it. Also, the males of my grandparents' generation showed a marked propensity, which is echoed here, of favouring the male offspring, however much they rely on the female relations for their care and maintenance.
Does any of this strike others as true to nature?