Yes, its possible if your service provider can provide you with message logs. But generally these call logs are not available to general public.
If you are using Android phone, you can use Android data recovery software. It is widely available for Android, but unfortunately not for iOS
Depends on the APP you're using. Some apps delete the messages in your inbox only.
If by any chance you sent it while offline and then deleted it, then no the other party won't receive said message.
Yes, its possible if your service provider can provide you with message logs. But generally these call logs are not available to general public.