First thing first: next time you post a picture, make it smaller, it's a pain in the rear reading your post left-to right. 
A few topics down someone asked a question much similar to yours. This is why it is important to skim through this forum, because you'll find tons of info and answers to your questions.
Also, buy a book or do as much research on iguanas as possible.
Moving on. Iguanas get most of their water from vegetation, frutis, and rain-water dripping from the leaves. In captivity, the same is applied. Some do drink from water bowls, others do not. As long as the animal is healthy, don't worry too much, and keep water available at all times. Letting a couple of ice-cubes melt and drip can help stimulate drinking.
Since the iguana is new, it is only natural to view you as a potential predator. Also, when you're holding it, it may not be so "cute and sweet" as it seems. Iguanas, like many animals, close their eyes when scared, to sort of "block" the threat. But it is good to know it falls asleep in your arms... that's a good sign that it is slowly understanding you're not a predator.
However, keep in mind iguanas are not like puppies. You can't expect to take one home, and immediately have a perfect exotic pet that will eat, drink and socialize when wanted to. Nearly all exotic pets are somewhat difficult and problematic. It is also wrong to assume all iguanas can be turned into the cuddly ones seen in books or read from Reptiles Magazine (a great mag to subscribe to).
Patience and positive reinforcement are the key. And, don't force it to like you so soon. Let it adjust, eat regurarly etc. Further down you can find topics on the subject.
How big is the enclosure? It is properly warm and lighted?
Anything else, feel free to ask. But do your research! 
- IJ
p.s. Stewie is a k!ck-@$$ name for an ig!
