If the battery is dead it's a goner until you lay eyes on it again.
By calling your subscriber and having them do a gps locater on it. That should give you exact details unless it somewhere in your house
Unless you can retrace your steps and find it, I doubt it. I lost mine at a store once, the battery was alive and the phone was one. Someone turned it in and they tried to text a few folks in my contacts, but when a friend called it and a stranger answered it, only then did I know where it was. They held it for me. Otherwise, you'll have to get a new phone and have them cancel the old phone, and if it isn't in your contract terms, they may want to charge you the full price for the phone.