Yeah, I think all GCs make that little quacking noise.

Cody does it all the time! It's definitely really cute! And as far as the biting goes, this is what I did with Cody... Not everyone agrees with this method, but I used the 'earthquake method'. Whenever he would bite me (he, like most green cheeks, was a VERY nippy baby), I would just wobble my hand to make him feel slightly unstable. This would make him release, and after only a few days, he got the picture and stopped nipping completely. Didn't hurt our relationship one bit, and it was effective. But for some reason, many people don't like this (and it's not shaking the poor bird, it's just a 'wobble' to make them feel off balance).
Other then that, you could try putting him down and turning your back on him whenever he bites. This may work to, but might take a little more time. And as for the screaming, I had trouble with Cody and this as well. First moving his cage helped a little bit, but I also made it 'special' for him to go back to his cage. Cody LOVES his seed, but doesn't get a whole lot of it, so I only give him seed when he goes back to his cage. He is almost always eager to go back into his cage now, because he knows his favorite snack is waiting for him.

You could try that and see how it works. And it doesn't have to be seed, just anything he likes. Just make sure it's ONLY given when he goes back in his cage, so it keeps it's specific value. Also, teaching him how to use foraging toys can also make his in-cage time more exciting.

Finally, and most importantly, never respond to his screaming. It will be near impossible to stop it if you do. But, I'm sure you knew that.
He is incredibly adorable btw!

What a face!