Can I develop ios 6 app using xcode 5 and ios 7 SDK

Question

1. I am currently using xcode 4. Is it easy and possible to develop ios 6 app using xcode 5 with ios 7 SDK?
2. Should I update to xcode 5 if I want to develop an app that both ios 6 and ios 7 compatible?
3. Will App store stop signing ios 6 app later on? Because I want to put my finished ios 6 app to app store later on.

Answer 1

1. Yes
2. Yes
3. No, You can work on Xcode 5 and iOS6.

You can simply update your Xcode 4 to 5.