I have the same intake, one from ebay...Here is what I found when putting it on.
First off, the hose to the fan housing (doesn't go to radiator) is just a resonator...Doesn't do anything. You can disconnect it and won't cause any problems at all.
As for the sputtering, check the seal around your maf....If that is leaking, it would cause the problem you are having. Anywhere between your maf and throttle body would cause that problem. The maf adapter that came with mine didn't line up quite perfectly, so I found one at auto zone that fit better. If your air lines are kinked, your car will die out. Right now, I am trying to find some silicone hose to fit on mine....the silicone they sent me is too small for two of the adapters on the air tube. I found a website that deals with silicone hose specifically...
http://www.stylinmotors.com/index.html
That tube from your air filter box is the aiv....Basically, it pumps air to the cad converter on your exhaust to help warm it up (or something like that)...You can take it and the little black box, as well as the other metal stuff that leads from the black box. Frees up quite a lot of space. If you do that, be sure to plug the three hoses you will have left after taking that off. The big hose leads to your exhaust, and your car will be REALLY loud if you don't plug it. Basically, just plug them all.
When I installed mine, I accidentally clipped a wire on one of the plugs right near the throttle body leading to the fuel injectors....Check those and make sure nothing like that happened, because it caused my car to die out instead of idling down properly....It sucked trying to figure out what was wrong lol.
Good luck.