Can my exterior shutters open or close? ie functioning

That's up to you! If they are installed as functioning shutters with hinges, they can be operable. This means they close over your windows for protection when needed. Hurricane shutters specifically are intended for this purpose and are typically found in locations that experience extreme inclement weather. Bahama shutters do just the opposite: they can be opened to allow more air circulation in hot climates.
On the other hand, fixed styles cannot be moved and serve as a decorative accent to your home’s exterior. If you live in a location that doesn’t experience inclement weather, these may be a more appealing choice since they tend to be more affordable as well as much easier to install.