Is it possible to develop an app only for me and my friends?
Just make the app and upload it directly to my iPhone.
Yes. You'll need an Apple Developer account which costs 99 USD a year.
It depends. If you have an Apple Developer account ($99 per year), you can create either a ad hoc distribution profile or use a development certificate. For more information on that, view here. Although it is called beta testing, it serves your purpose.
Now if you don't have an Apple Developer account, you can use jailbroken devices and Jailcoder. To use this method, follow the steps below:
An older video: http://www.youtube.com/watch?v=3NAm1MOGabw. Ignore the fact that it says Xcode 4. It works on Xcode 5.