I have an electric vehicle, does my inverter or battery have to be next to where I charge my car?

Not necessarily – Your EV might be charged from a wired-in charger or power point connected to your electricity switchboard. Your solar and battery will be connected to your switchboard. 

If your EV charger supports integration with Solar/Battery system you will be able to charge your car using power from your solar or battery when needed, even if your car and battery aren’t close together.