Question 1:
Humorous passage 1: "It (the umbrella) was made to be carried on the arm like an enormous ornamental bat and to allow one the opportunity to put on British airs as the atmospheric conditions demanded."
Humorous passage 2: "(The umbrella is) An item to be carried in the street, to be used to startle friends and—in the worst of cases—to fend off one’s creditors."
Question 2:
Passage 1 is funny because it compares the umbrella to an ornamental bat, which sounds weird in the first place. Plus, the umbrellas is said to be used by people who want to seem British, which is even more outrageously funny.
Passage 2 is funny because it treats the umbrella as a scary object which can be used even to fend off people you owe money to, which is absurd.
In both passages, the author uses tone and voice in a very witty way: he speaks seriously about absurdity, about unimaginable stuff. It is like an encyclopedia of weird and fun facts. That is what makes it funny: the contrast between a serious tone and larger than life images.