Binary Tree All Paths, Max Sum Path, Diameter, Longest Path, Shortest Path, Closest Leaf

Given a Binary Tree T.
1. Find all paths from root to each of the leaves in T.
2. Find the longest path from root to a leaf (also called Max Depth or Height of the tree).
3. Find the path that has largest sum along the path in T.
4. Find distance (shortest) between given two nodes in T.
5. Diameter of T or Longest path between any two nodes in T.
6. Find mirror image tree of T.
7. Find min length path that sums to a given value.
8. Find the closest leaf from root.