"Yesterday we shared a banana"
I love sharing bananas with Xander - I get a kick of how he eats them! Just be careful when you do it so you're not both biting off the same end. His saliva could potentially make you sick, and yours could make him sick.
"I hope someday i can get Nemo to be that tamed."
Just keep working with him. It took Xander over a year to become completely tame. I live by the 'handle him a lot!' rule. One of the things that helped me was that I started giving Xander a bath every morning before work. I filled up the tub was warm water (about 88F) and let him soak in it until he pooped. When he was returned to his cage, he returned to find his food dish full for the day. This ensured that he was handled every single day at least once and that the experience had a purpose for him. Small igs tend to be afraid of water at first, so if you try this remember to only put a tiny bit of water in the tub (just up to his chest) and to take him out as soon as he poops so that the whole experience is rewarding. You might even try putting a washcloth in with him so he has something to hold on to so he doesn't feel so overwhelmed.
The other obvious advantage is that it trains them to poop in the tub, and they do learn very quickly. Small igs will poop 2-3 times a day, so if you want him to be completely trained, you'll have to poop him in the evening, too, or at least supply a large enough water dish for him to poop in. But it's worth it. By the time they hit about 2 ft, they're only pooping about once a day and it's much easier to clean the mess up. Just make sure you clean the tub out really good and disinfect it after each time.
"Nemo lives in a 3 foot by 1 and half foot tank. It is 2 feet deep. He has 2 big logs in there to clime on, a hot rock (for decoration only!!! I know how bad they are for igs) and a UVB light and heat lamp in his basking area."
Well, it's definitley a start! In tanks, it can be hard to get the temperature gradient just right. What are your temps, both ambient and basking? And what is your humidity? It's really important that you know; you should have at least one hydrometer and at least two thermometers in your set up.
It's great that you have a UVB lamp. Just in case you didn't know, UVB is filtered by fine mesh and glass, so, ideally, there should be absolutely nothing between the light and your ig. It should also be no farther than 6" away from him, so you may need to play with your set-up to find ways to bring him closer to the light.
This size of tank will only fit him comfortably for the first year. It's never too early to start building a permanent home!
"It's g Fresh water everyday, and his diet consists of salades of Carrot, yellow squash, turnip greens and collard greens. He occasionally will have a banana and strawberries."
It's definitely a start. Think variety. You're on the right track with the veggies and collard greens, but you should add even more dark, leafy greens. The greater variety you give him, the healthier he will be. Here are some examples of excellent veggies to give: mustard greens, turnip greens, dandelion greens, arugula, endive, watercress, green beans (finely chopped), butternut squash, kabocha squash, peas and the very best fruits are papaya and fig, if you can find them.
This is what Xander is getting today:
collard greens, red dandelion greens, mustard greens, watercress, arugula, cilantro, kale, green beans, red bell pepper, kabocha squash, and calcium.
You should also consider adding a vitamin and calcium supplement. I use RepCal's Herptevite and RepCal calcium with no added vitamin D or phosphorous twice a week each. Do some more research about ig nutrition before you decide what you're going to do, but you should at least have a calcium supplement to help prevent MBD.
"As far as handling goes: I handle nemo about 3 to 4 hours a day. He has been showing amazing progress whenit comes to taming. He no longer tries to bite or whip, but he does still run and wriggle when i first hold him."
Good. The running and wriggling is partly because you're keeping him in an aquarium and can't help but to grab him from the top. Some igs just don't like to be grabbed, but settle down soon afterwards. My 2-year-old still runs sometimes when I reach in to grab him, and his cage opens from the front. Just keep with it and you'll hopefully end up with a sweet adult.
Cute pictures, by the way 
He looks healthy to me. You should schedule a vet appointment if you haven't already, just to start building that relationship with your vet and also to get a fecal done, since most babies have parasites.
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~Alika~
1.0.0 green iguanas
0.1.0 cockatiels
1.0.0 senegal parrots
0.1.0 blue-fronted amazons
0.0.1 red belly piranha
