You unfortunately have broken enotes regulations by asking more than one question - you are only allowed to ask one question per day, so I have edited this question down and will respond to one element - the climax in this story. If you wish to find out the other stages of this story you will need to ask more questions.
It is important to remember that this story can be quite confusing for readers to understand because it employs a technique called flashbacks, when the narrator looks back at events in her life and the action jumps between these different times. The climax of the story actually occurred in the past, and the narrator is looking back and telling us about what happened. The climax of the story is clearly when the house caught fire and it looks as if the narrator is not able to escape and will die:
Outside, my mother stood below my dark window and saw clearly that there was no rescue. Flames had pierced one side wall, and the glare of the fire lighted the massive limbs and trunk of the vigorous old elm that had probably been planted the year the house was built, a hundred years ago at least. No leaf touched the wall, and just one thin branch scraped the roof. From below, it looked as though even a squirrel would have had trouble jumping from the tree onto the house, for the breadth of that small branch was no bigger than my mother's wrist.
It is this climax, when the narrator is apparently facing certain death, that gives the mother the opportunity to use her amazing agility and talent as a trapeze artist to make "the leap" that a squirrel would have struggled to make and rescue her daughter. Now I have identified the climax for you, go back and see if you can identify the other elements of the story. Good luck!
You didn't say how you are going to focus your analysis. I'm guessing that it is probably connected to either theme or character.
First of all, I would check out the enotes section on "The Leap" to help you get a sense of the themes:
On its most basic level, it is a pleasant story of a daughter doing her duty by an aging parent whom she loves and respects. On a deeper level, it is a commentary on to what one owes one's existence and what one makes of it. On yet another level, it speaks of the moments of decision in each person's life, and the ways in which one uses these moments to change the courses of one's own and others’ lives.
A good thesis is:
- arguable --that is, something that you can defend in your essay. If it isn't, you'll have a hard time writing it
- insightful--it should show that you see something that not everyone else does
- important--that is, it is not too obvious, and it is worth the time and attention you give to it
- in a sentence
Your first attempt seems too obvious. If anyone who read the story knew that the daughter respected her mom, then it's not worth while writing about that. What else do you see in their relationship that connects to the bigger themes? Can you find one way of looking at them that reveals some insight into the way people build respect/ trust in relationships? Or a way that shows, through the interactions of the characters, that in moments of crisis we reveal our true character, as the two of them do?