Hello everyone. New member here!

So i got a new tiel on monday morning from a pet store. It's not tamed and was living in a rather small box there (made out of glass). I bought him the largest cage possible there but it's still a bit too small..i am getting him a big and comfortable one today and some more toys.

He is pacing and doing a flock call all day. He lived next to a bunch of budgies in the other box. Could he be missing them?

He calms down for a bit if i put some classical music on (he seems to like Vivaldi haha!). I can't really understand his body language.... Sometimes he sits on his perch and lightly shaking, but simultaneously he grinds his beak with the feathers around it puffed up, which is supposed to be a good thing.
Yesterday evening he played around with his toy for a bit.

He sleeps quietly trough the night. He didn't seem to have any night frights yet, as my room isn't completely dark and is relatively quiet and away from busy street. I have some decorative lights hung above my window that shine troughout the night so i guess it's like a night light to him.
In the morning he keeps quiet for a few minutes before he completely wakes up. Then he gets a drink and starts his usual pacing and screeching.

I haven't attempted to put my hands on him yet, just change his water every day and make sure the cage is clean. Otherwise i just sort of hang around in the same room, occasionally talking to him. He seems to be interested in me. He comes up on the perch when i talk to him and looks at me. Of course when i am changing his food and water he runs to the far end of the cage. Poor thing.

I have seen him drinking water. He drinks in the morning and then in the middle of the day.

The problem is i haven't seen him eat anything yet. Not even the millet spray i have hung in his cage.
I am worried he might get weak.

I put a couple of goji berries and a raisin in his bowl as a snack. This morning i found both goji berries on the floor haha. Maybe he did eat a bit when i was out?...

The other question is, should i let him out to fly? I want him to have some excercize and explore the room but i am worried i will stress him out if i try to put him back in his cage.

What can i do to make him feel comfortable and welcome in my house and adapt better?

Thank you for reading.