You are doing great with him. Quite honestly, if it were me, I would not be concerned about playing videos, bird sounds, or the music, or even playing TV for him. I have homed budgies for many, many, years, and they are a very easy and hardy species, once they get to know you. I have found that mirrors and swings and music, or YouTube videos or TV does not affect them or their hormones when they get older, like some other species.They love it. And, your idea of using his night cover folded up is perfect. All birds, at times, revert back to previous behaviors. One day they may be open to allowing us to touch and play with them, and another day they may be less willing to do so.

Most budgies do drink water as they should, but they do not drink a lot. Get some fresh leaf lettuce, if your parents do not mind, and chop some up fine, or hang a leaf in the cage. Lettuce has a good amount of water in it, so that will hydrate him. But also, it may make his poops rather loose so do not worry if you see them like that.