Is it possible to teach degu to sit on my shoulder and don't go away?
It is possible, it just needs a lot of patience. How to teach the degu: to sit with it on the couch or something soft, so that possible fall wouldn't be dangerous. Unfed degu sitting on the shoulder then give some food (normal food better than treats, so that the degu isn't overfed by unhealthy food) and talk to him nice to make him calm. Repeat this again and again until degu can sit safely on your shoulder (keeping the balance with the tail). Then you can try to slowly get up and walk the house. Degu can learn sitting on shoulder safely so that you can walk with him, like with rat.