Can't answer the first question, but answering the second, the elk are only on the refuge in winter months. Winter having barely even happened this year, the elk have already been on the move away from the refuge to their summer grounds - some of those inside Grand Teton National Park and others into the national forest lands eastward. Apparently the Yellowstone elk almost never use the refuge but have their own areas they frequent in the winter.
If you visit Jackson in the winter, there are fun tours of the elk refuge, in large open sleighs drawn by horses, which can get you quite close to the elk in a safe manner.
