While it is 'possible' to write iOS apps outside of XCode, I do not know how you will test, debug and sync your iOS application to a iPhone without XCode (which means you will need a Mac).
You will need to register a developer account with apple, and then what usually happens is your iPhone gets marked as a developer iPhone and is attached to your account (thats how it used to be anyway). Like Ramhound said, take a look at Visual Studio (I do not have any experience using Visual Studio to interact with an iPhone, so can't really help you there). The XCode IDE has a lot of tools to assist in developing software for iOS and OS X that I do not think will be available to you unless you are using a Mac.
After taking a quick peek at the mono project, it looks like you should take a look at Xamarin.iOS.
Xamarin.iOS provides full access to iOS APIs. Take advantage of the entire spectrum of rich functionality supplied by the latest version of the platform.
Keep in mind in order to do any of this, you will need a good understanding of Objective C and/or software development skills in order to get too far. I tried my hand at it an failed, but your mileage may vary.