He loves Millet and he does try to get it I think he's doing it on purpose because sometimes he will and then hop off right away after he gets his reward and then sometimes he just won't at all but anywhere outside the cage he's ready to do anything1. I believe you just continue to play it around him and if you notice he has started to pick it up you work on it more with him by encouraging him to sing it with treats. I'm not certain that is the best method, maybe owners with male 'tiels can be of more help with that? But I believe it is just repetition, a lot of it. Once they start singing it they looove singing songs though. So be prepared to hear it for a while!
2. When they love being around you and spending time with you. Sometimes they may follow you to another room or call for you when you're not around. They will cuddle up next to you and preen you or sing for you.
3. I think you have said you have tried this, but does he have a favorite food that he likes? You can hold it just out of reach of his mouth so that he has to lean forward and grab it. Make it so that he has to lean far enough forward that the only way to get the treat he loves is to step onto your hand. Then let him have the treat while on your hand and tell him he's the best. I held a treat for Kiwi like this every day for hours until my arm cramped up trying to get her to do this and eventually it worked. But first she had to accept eating treats out of my hand. If your 'tiel will already eat treats out of your hand then this may work.