Budgies by nature are super active, which means they are happy and healthy. btw. They love flying, he is training his wing strength. Only sad and sick budgies are inactive all day.
This has also been happening to myself. There are two wall lamps in my front room, and my budgie flies backwards and forwards to each one several times before stopping and becoming more relaxed. I don’t know why they do it, but Im sure its nothing to be worried about.
Hello, bobbing head for budgies is normal behavior. When Budgie bobbing head that indicates she is happy and excited. She just likes you 🧡
What kind of small house? If you have a small house inside a budgie cage, it’s better to remove it. She may lay eggs, infertile eggs (If you don’t have bonded male). It’s not vise to have anything associated with the budgie nest box inside the budgie cage.
She is missing flight feathers. It takes more time to grow flight feathers, but it’s better to consult your vet. It is better to know if there are any health problems with her wing. Good luck
Do you have a female budgie? Also, Male budgies like to bite for playing, you need to provide more toys, foraging toys for your budgie.