For a balanced binary search tree what is the worst case case time complexity for accessing all elements within a range of nodes?
One way to do it is to construct the tree containing those values:

Explore the BST until you find the root of a subtree that is between the bounds;
Explore the left part of the subtree, and trim branches on the left that have a root $\leqslant node_x$;
Do the same thing on the right for roots $\geqslant node_y$

Each of those steps are done in $O(\log n)$ since the BST is balanced. Once you have constructed the tree, just do a tree traversal (in-order for example) of it. This last step is indeed done in $O(k)$.