Character analysis is essential as it is meant to indicate what you have learned about the characters in the novel. The letter format itself is secondary. However, letters are usually in block format in which each main idea is in another section of the letter without indenting or paragraph form in which main ideas are in new sections and indenting is used.
After that, letters are essentially like essays. Clear beginning, clear middle, clear end.
Another approach to this, outside of form and structure, would be to become involved in the characterization of each in the letters. Remember that a letter, such as the one you are being asked to write, is a written reflection of the character of the person. This means, when you are writing a letter from Stevens' point of view, you will have to "get inside his head" and figure out how would he write to Miss Kenton. Some questions to ponder:
1) What would he ask of her? What is it that Stevens would ask of her?
2) How would he approach it? Would he be direct in asking her what he wished to ask her, or would he kind of allude to it in a "hit and miss" fashion?
3) How would he conclude the letter? Certainly, the conclusion of the letter would have to be replete with what Stevens would consider his "higher calling." What would that be for him?
The same type of analysis would go for Miss Kenton. The most important element in writing letters in the persona of characters from novels would be that you really begin to understand these people as exactly that- people who are real with valid and authentic emotions.
Your grammar book will probably have a section on letter writing, but there are also lots of places online that will help you format and punctuate properly. Below is a link that will lead you through either friendly or business letters.
For the message of both letters, you'll need to revisit the book and put yourself in the shoes of those characters. What would they say to one another?
Read the book again and notice how the characters talk. Try to imitate that way in writing a letter.