IPhone – Is the Shown location of your phone on find the friends accurate if the the phone is offline

This is most likely the carrier intentionally deactivating the old SIM.

When iPhones first came out, your current phone would normally get deactivated at the moment you purchased a new phone and told the carriers to move the service to the new phone. Now, they wait until the new phone checks in to perform the swap to account for delivery delays, backups, etc...

Your first step should be to contact the carrier and explain that you want service on both phones and arrange for which number rings to which device. They might be able to accommodate this over the phone, but if the old SIM has been deactivated in the networks, most carriers are very unwilling (or unable) to re-activate the old SIM and instead ask you to get a new SIM from them at a convenient local retail spot or by them shipping you new SIM card(s).

Apple's restore process and activation of the device doesn't affect network activation and for locked phones, you just need a SIM for the correct carrier to activate the device. iOS does not check or care that the contract is expired, not established or live for iOS activation - just that the SIM is manufactured for the correct carrier.

Lost mode combined with iOS 7 is extremely useful as long as th phone has cellular service or is connected to WiFi networks that it trusts. The device needs to connect to the Internet to be re activated after wiped, at which point it will enter lost mode and refuse to work again without your password for Apple ID.

Be sure to not remove that device from your account since that makes the device far more risky and expensive to sell, pawn or try to use by the thief or even someone that ends up with the device. Someone could desolder the CPU and try to reserialize or cannibalize the parts, but the quick hit of cash for a stolen device is defeated by Activation Lock and Lost Mode features.

The device shows as offline when it hasn't checked in recently to the Apple servers despite an attempt by the Apple Push Notification service attempting to send a check in request to the last active address of the device on the Internet.

If the device ever gets connected to Wifi or cellular data reconnects it, your Lock request will get sent, acknowledged and you'll get an email. If you are quick, you can log in to find my friends and see if the location data updates as well at that point.