The first thing you described is nothing more than what you think a strech. This is totally normal.
The second one sounds like it is just something fun that he likes to do. While not all birds will do stuff like that it is nothing to worry about.
Alex loves to sit on my hand flip upside down and normally will preen. Sometimes he will flap his wings or strech. He will also filp and I will swing him saying Weee while walking with him back to his cage when I have to leave. It makes having to go into his cage fun.
We also have a game that he mostly made up when he was a young baby. I will flip him upside down over a table and he will strech down and pick up a toy and I will flip him back up. He loves this. I work with him on his colors this way. I have some of the baby links that are solid colors and will have 3 different ones for him to pick from. I tell him what color I want him to get when I filp him. If he gets the right color I get excited and tell him Woo-Hoo! good bird. He made up the game I just use it to teach colors while having fun.
While it is to bad that your baby was clipped it's not permiment. The flights will molt out. In the mean time it will let you and your baby get to know each other better and earn each others trust.