I have a Moto E 2nd generation that is broken. Can I use the SIM from this phone to swap into an unlocked phone or do I need to order a SIM for the unlocked phone?
No the SIM card cant be swapped like that between these 2 phones.
You can order a SIM card, but first verify your Moto G4 will even be one that is compatible for a Republic SIM by following instructions found here:Bring your own phone to Republic! | Republic Wireless