Considering he is around 5 months or older you are doing very well to have tamed him as he seems to be right now. You have created that special bond already and its all positive from here on. Many petshops and bird dealers sell older budgies as babies, especially if they clip their wings and they cannot fly...its easy to say they are younger when someone doesnt know.
But not to worry, you seem to have won Billie over and all is good. Glad you are here.
Thanks, KAZ.
Although, on the other hand, I have reasons to believe he truly is 7 weeks old.
I believe he has matured a bit early, but is 7 weeks all the same.
It is probably hard to tell through photographs, but I think he is definitely a baby.
Thanks again for the info, and the friendly welcome, though!
~ Billie and Steph.