Watch some of the YouTube Disco videos of when and how his owner taught him to talk. She got right up in his face and use tons of expression.
Yes! And it's really fun to experiment with this! Trying different notes and sounds and watching their body language to see what they react to! It's really different than dogs and cats, I'm amazed every day. When people say budgies are "skittish" it really does seem to be motion-specific (being a tiny prey animal that goes to ground to forage they need to be especially vigilant to when they need to take upward flight). Volume or excitement of tone only seem to upset my guy if they are coming suddenly out of silence-- he deals better with new sounds layered into familiar sounds. I might work to determine a comfortable distance (the closest you can get before the bird tries to make some motion to step away from you or tense for flight), then pause there and sing and chatter away. Anything that reinforces presence =/= threat. And know that some motions (like passing anything over their heads) can be instinctively taken as a threat no matter how much progress you've made or how comfortable they are with your hands.
My guy was hand-tame (but parent fed), like your other bird, but he'd had zero human interaction for a week or so before he went home with me. On his first night (after a four hour drive and no evening meal) he flew up in a panic to perch on my closet door. I moved like molasses-- the way I'd move trying to observe a wild animal, but kept chattering away, and was able to move the object he was sitting on over to his cage. Before I even
tried to move it, though, I just sat underneath him and talked and talked in a chipper voice, until I saw a significant change in his body languge. I'm learning from each day and from the experienced folks here that even when it seems like nothing is happening, a lot is going on in a bird's mind. You mentioned yours wouldn't take millet with your hand in the cage, but every
second that passes without her moving away from your hand is a second she is learning that you aren't a threat. The stakes are so high for her! If she is wrong about you, that means instant, inescapable death. The longer you can stretch out a peaceful moment, the more you are reinforcing her cautious trust in you.
What do you remember about taming your first bird? I'm really curious about the differences because my guy is hand-tame, and I have considered adding another a year or so down the road.