Hi ALK, welcome to the forum

In answer to your first question, well..I wouldn't be taking him outside even now! It's way too risky.Theree's no telling how fast he might suddenly take off. He could only be able to fly a little distance one day and then suddenly he's flying waaay better than the day before. If he got to a tree and climbed up, how would you get him down? And certainly when he is able to fly better, there is no way to stop him from flying off.Even if he wanted to come back to you, there is a chance he could be caught in a wind current and carried further away. Not to mention predators outside like cats dogs other large birds?
You can however teach him to come to you INSIDE when you call him or do a certain whistle

#2 lunging and biting? Usually if a budgie lunges or bites it's because he is feeling threatened. Try backing off a little..let him come to you. But if he does bite, try not to react by pulling your hand away quickly. Act like it's not bothering you. Otherwise he will think hmmm if I bite the big bad human will leave me alone! LOL You have to work slowly and earn your birds trust. You can't force him to be friendly or sit on your finger.
Even tho your baby was hand raised and used to human touch,you and your home is new to him.
I don't see anything wrong with him being by a window, other than making sure there is no draft, and if it's sunny out he doesn't get too hot. He needs shade

If you mean that you leave his cage open even while you are gone, I don't think it's a good idea because he could get hurt or stuck behind something and you wouldn't be there to rescue him.
Some say that single birds might bond with the reflection in a mirror rather than with their human, but if he is bonding with you, I don't see a problem with it.
Takes you for granted?! But of course! I think they own US rather than the other way around! LOL
Oh man,naming?? I know, it's soo hard to come up with a name that feels right isn't it? Especially if you don't know whether it's a boy or a girl LOL
A close up of your keeter's cere might help us determine whether it's a boy or girl. From your avi pic I'm guessing you have a little boy

It's cere looks pretty dark purple? My Levi's looked like that at that age
