What were Harriet Jacobs s attempts to escape like and how did she finally reach the North? Were all of her problems solved upon reaching free states?

There are a few attempts at escape culminating with her eventual freedom. Check out this short GradeSaver summary and you will get a good idea about her escape attempts and her final freedom.

http://www.gradesaver.com/incidents-in-the-life-of-a-slave-girl/study-guide/summary