You started handling him about 3 weeks too early. Normally in this situation I would say that his "calmness" while being handled is in reality petrified fear, but it seems like he might have become accustomed to you to some extent. I don't know whether to say stop handling him for two weeks to let him get more accustomed to his new situation, or to say keep handling him because he's made a start with taming.
I assume he closes his eyes when you touch him. It isn't a sign of enjoyment, it's him trying to reduce his exposure to unwanted stimuli. Iguanas do give up even though they are repelled by handling.
You should stop handling him for 3 weeks. Give him as much peace as possible. Try to be unobtrusive when you feed him. But his views of you and others walking near his habitat are a good thing and he will get used to it. Even the noises in your house scare him right now, and I think the handling has delayed his acclimation.
Try putting aromatic treats in his cage, like bits of banana, when you come close. Use a long skewer or 1/4" sharpened dowel from the hardware store to quietly place them near his snout. He might start to associate treats with your presence. It will take him a week to get up the nerve to try a taste and learn to like it. Be very patient with him, he's not at all like a puppy who loves attention, but rather is a genetically mandated loner who runs from anything new. I think this 3 week period of relative peace will reduce his stress, cutting down on his cortisol levels, and let him eat better and learn to drink from a bowl.
You will eventually need to pick him up to start his training. Learn to grab him quickly to avoid scaring him too much. Don't be afraid to use a firm grip because his body is very tough (except if you handle, bend, or even touch his tail he will probably drop it). Ignore any biting or whipping. He is too young to do much if any harm to you, and if you react by dropping him he will forever know how to defeat you and get away.
Enjoy the sight and the behavior of your little guy while his color is still bright blue :-).