When I try to run an app on connected iPhone I get the error: "Could not find Developer Disk Image" I am not registred Apple Developer right now, but you wouldn't need that in xcode 7 would you? I Just updated xcode to version 7.2.1 and my iPhone (6 plus) is running iOS 9.3
Xcode 7.2.1 currently only supports up to iOS 9.2
9.3 is in beta, and requires Xcode 7.3, which is currently also in beta. You can download from the developer portal. You won't need to be a paid developer to do this.