The analyses of a text #3

The narrator recalls his adolescence.
After the funeral of his old nurse Peggotty's husband, he visited Peggotty's elder brother Mr. Peggotty's house to dinner.
Mr. Peggotty's nephew, adapted son Ham was due to come with his niece, Ham's fiance Em'ly but Ham came to alone.
Em'ly fled with the narrator' best friend Steerforth with leaving a letter to Ham.
Mrs. Gummidge was Mr. Peggotty's late best friend's wife and after her husband's death she lives off Mr. Peggotty.

As to deploring her misfortunes, she appeared to have entirely lost the recollection of ever having had any. She preserved an equable cheerfulness in the midst of her sympathy, which was not the least astonishing part of the change that had come over her. Querulousness was out of the question. I did not even observe her voice to falter, or a tear to escape from her eyes, the whole day through, until twilight; when she and I and Mr. Peggotty being alone together, and he having fallen asleep in perfect exhaustion, she broke into a half-suppressed fit of sobbing and crying, and taking me to the door, said, 'Ever bless you, Mas'r Davy, be a friend to him, poor dear!' Then, she immediately ran out of the house to wash her face, in order that she might sit quietly beside him, and be found at work there, when he should awake. In short I left her, when I went away at night, the prop and staff of Mr. Peggotty's affliction; and I could not meditate enough upon the lesson that I read in Mrs. Gummidge, and the new experience she unfolded to me.
[David Copperfield by Charles Dickens]
1. I'd like to know why it is "observe her voice to falter," not "observe her voice falter."
2. I'd like to know the clause in blue means "In short when I went away at night, I left her with the prop and staff of Mr. Peggotty's affliction."
3. And I'd like to know what "the prop and staff of Mr. Peggotty's affliction" means.
Thank you in advance for your help.