Question 1. The answer is perfection. This is made clear by the narrators obsession with the beauty and perfection of the white umbrella.
Question 2. The answer is because she had to work late. The story clearly states that their mother wasn't going to be on time because she had to work.
Question 3. The best answer I can come up with is that she knows her feelings of shame are inappropriate.
I gave the answers to questions 4 and 5 in the comments.
Hope this helps!