Sadly, with birds you have to learn to take bites. I've had my new guy for a few weeks and after the first three days of time outs for biting, I used my body to lean into his cage door and shoo him in closed the cage, covered him and ignored him for fifteen minutes. When he was calmed down, I let him out to try again. He now knows and even says, bite is bad boy, bad bird. No bite is good boy, good bird! Yes! He learned fast not to hard bite where he left bruises. He still nips, but it isn't too painful. He only nips during training, that is to be expected. I can now rub his head and get him to step up on my finger rather than my arm. He loves it most when I just let him sit on me as I talk to him. He listens intently and sometimes says something to me.
If he is on your shoulder and you want him to go into his cage, lean down with your shoulder pointing into the open door, say, go home or go to bed. You may have to shake a little. When he goes in, praise him. After a while, you can play the finger game and work on being able to rub the back of his head. For now, talk to him calmly and gently. When he bites, calmly say, no bite. Put him in time out. If you jerk away or raise a fuss about a bite, they can find it amusing or just like the reactions you make and want to bite more. Some are just in the bratty, need to test their boundaries stage every so often. Jerking away also teaches the bird that if it doesn't want you to do something, the solution is to bite to get what they want.
A beak is like a hand, they will use it to explore. If the nipping doesn't hurt or pinch and is more of a nibble, he is likely grooming your face. He could also just be exploring you and may pinch a little hard, to test your reaction, try to be calm and say, no bite. Jazzy now grooms my face and when I ask for a kiss, he moves in close to my face, makes a kissing sound, opens his beak and licks my lower lip. If he is not on me and I say something about a kiss, he says, kiss and makes the sound. Grooming is a sign of affection. The best thing to see is him sitting on you and grooming himself. That means he is comfortable with you. When he does this, you can work on the finger game. It sounds like you are doing great for a start. Try looking at him and just talking. He may love the attention and will calm down more. Go to a room where his cage isn't in sight.
I'll explain the finger game a bit later, you might want to consider clipping his wings for target and step up training. After he learns bites lead to time outs, when you work on finger training, he wont bite as hard if you pay attention to his comfort level. He'll nip, but slowly he'll trust that finger and want to play with it and even want you to pet/groom him. It takes time and work though.