make sure that you are putting in the password correctly. That's basically the only thing that would cause problems since the iPhone does not have any other settings. Or at least not until after you connect.
The only other thing it could be is the wifi card is malfuntioning. Test by taking the security off. if you can connect like that, then change your password to something you can type on the iPhone easily.
could be either. Most "N" routers have settings for either a "mixed" network that is compatible with b, g, and n devices, OR you can set them to "n only" which will boost the performance.
I have my Time Capsule creating an "n only" network, and my iPhone sees it as available, but will not connect.
this is why i hop Apple will introduce an N receiver into the iPhone soon... while it won't benefit in the performance at all (unless they also add wifi-syncing), it WILL promote smoother 802.11n use overall, which is important for other Apple products like Time Capsule and Apple TV.