One major conflict Anne has is depression. She is constantly fighting this conflict. Nothing can make her happy. It still hasn't been resolved.
The major conflicts during this book is the Jews vs. the Nazis. The Nazis are constantly kicking the Jews out of their homes. They are then taken to camps and killed.
Anne and Mrs. Van Daan constantly argue in the "Secret Annexe". Mrs. Van Daan is always correcting Anne and saying how awful she is. Anne doesn't take that and stands up for herself which gets herself into more trouble.