False: the following tree has subtrees of the same height, but is not AVL, since only the topmost node is balanced:
Node 0 5 / \ Node 2 4 Node -2 6 / \ / \ Node 1 3 Leaf Leaf Node -1 7 / \ / \ Node 0 2 Leaf Leaf Node 0 7 / \ / \ Leaf Leaf Leaf Leaf
True: to preserve the AVL property, it might be necessary to rotate the nodes which requires a constant number of additional steps.
True: The two subtree can have at most height 1, so they height cannot differ by more than 1.
True: A degenerated tree has the same shape as a tree. It's height is propotional to the number of nodes.