Yes, the Atom Feed is only to update the App Store with the new issue information. The way to get your issues info is up to you.
You can send other data with content-available:1, for example a unique id of the issue that was just released. For example:
{"aps":{"content-available": 1, "sound":"silent.wav"}, "issue_id":"latest_issue_id"}
(I've added the sound component because of a bug in iOS 7 silent push notifications, read here.)
Yes, it's optional.
The background loading should be called on both - (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
and -(void)application:(UIApplication *)application didReceiveRemoteNotification:(NSDictionary *)userInfo
. One will be called when the app is awaken (after not active state), and the other while it is in active or background state. (again be careful when testing with iOS7, it doesn't work exactly like that for now, waiting for iOS7.1...)