I would like to develop iPhone apps without using Mac OS X. Is it possible to do this on Windows OS?
Nope, you have to use a Mac. All the tools are on the Mac, as is the simulator program you'll need to test in.
Even if you could somehow finagle the whole thing running in Windows you still need a Mac to submit to Apple to get it on the App Store.
Cheapest scenario you're looking $699 for a Mac Mini and $99 for the iOS Developer Program (which you won't need until you want to run the thing on a real phone). You can go cheaper on the hardware if you buy it used but something to keep in mind is that it must be an Intel-based Mac running Leopard (10.5) or higher.
While you can't develop iOS apps on Windows using full-on Xcode, Objective C, and Cocoa Touch, there are some Windows alternatives that will allow you to develop apps. You lose the flexibility and power of the full programming environment and language, but it's no longer impossible.
Here's an article that lists a number of current options. It's not the route I'd go (nor the route I chose), but it's no longer impossible.
No it is not possible for full development and submission unless you want to run OS X in a VM on your PC.
You can develop, to an extent, on other platforms, but as far as I know you need a Mac to submit.
Not supported and borderline with piracy but if you dig on Internet you can find how to create a virtual machine with VMware that run OS X. I do not post the link here but using Google is quite easy to find a really well made tutorial about how to proceed with detailed instructions.
I did it before purchasing a MacBook Pro to test how a Web Application I have work on a Mac and so I also used it to install Xcode, if you have a powerful Windows machine the performance are not so bad, but it's useful just for testing and seeing how the different iPhone developer tools works, if you want to develop something business related your only real option is to purchase a Mac.
Yes, you can. Check out this website called macincloud.com. Most people are trying to install Mac OS to PC hardware, sometimes it works, the drawback for that is newer mac updates often break the installation. macincloud.com actually allows you to rent a mac and access the Mac remotely. Therefore you always have the latest Mac OS and it is a good way to start developing iphone apps right away since you are actually using a native Mac system. Hope that helps.