Since enotes allows students to ask only one question at a time, I will address the first of your poems, "Cousin Kate."
I am not sure if I would consider the beginning of Christina Rosetti's "Cousin Kate" exciting in the usual sense of that word; the first stanza of this poem does, however, do a great job of capturing our interest and entincing us to continue reading.
First, there is the disonnance between the narrator calling herself a "maiden," but also describing herself as "hardened by sun and air." The word "maiden,"--to me, anway--conjures up images of curly locks, clear eyes, fair, soft skin, gentle laughter--anything but a creature who has been "hardened" by anything.
The poet continues to rouse our curiousity with the phrase, "Not mindful I was fair." We immediately begin to wonder who will discover that this "cotton maiden" is, in fact, "fair" and beautiful, and what will ensue as a result.
The phrase, "a great lord [did] find me out" suggests that there is some mystery involving this maiden, which of course further piques our interest.
The end of the stanza, which states that the lord "fill[ed] my heart with care" hints that our protagonist is not only mysterious, but tragic as well.
At this point, we are hooked. Who can resist reading a story about a girl who is beautiful, tough, innocent, mysterious, and tragic?