I need to write a letter. Can I print out the contents of the letter first and then send it to her? No handwriting. Is that polite? Why?

There is no question of politeness, but sincerity. There is a saying in China that "seeing words like faces". Some people say that a word is a person's second face, and there is another saying that it is clear when faced. These words mean that people can see you, but when they can't, they should show their "second face" and make them feel "dignified". Although the printed things are neat and beautiful, they also rule out your "sincerity".