In my first application version, I didn't implement the push notification, but I will implement it in the second version, my question is when I create an Identifier to publish my application in app store, shall I check the push notification service? or not?
Changing your AppID later in the future will work, unless you are using a wildcard character (*) on it.
If your AppID is something like:
com.me.myApp
Will work, but something like this:
com.me.*
Wont
So just be sure your AppID is correct.