Could I build app for AppStore under iOS6 SDK after iOS7 will released (Sept 18)?
You can, but I don't know how long.
Should (and can) I use XCode 4 for posting to AppStore after iOS7 will released?
You may use either XCode 5.0 or XCode 4.6
Could I use XCode5 for build app for AppStore with iOS6 SDK?
I think you can't.