Only if they are functional and not just decoration screwed to the walls.

The house would shudder to have shutters. The black and white attempt to simplify the complexity of it is in its bones. It would look ridiculous with more added on froufrou.

No. Notice that the similar neighboring houses don't have shutters.

You don't need shutters you need landscaping and decorating.  Put a bench or seating on the porch, add planters to the porch.  Add some color to the perimeter in terms of flowering plants.  No need to mess with the facade, it already has enough going on.  
Good luck and congrats on your new home!

No shutters and beef up the support posts, painting them trim color.

For the back of the house, stain the deck the color of the house, beef up those support posts and add climbers. Suggest Manhattan Euonymus. Start small and within a couple of years you will have gorgeous growth. Stays green year 'round, has a flower and a berry.

I would go as it is. Here is I tried some visual with blue

Black

and matching wood posts and brick