The third photograph makes it look like the shutter is warped. Is that true? If so, that is probably NOT what they are supposed to look like.

I don't think they're warped it is more of the hardware on the bottom is pulling it back too much.

they are made to look like they actually function. that is a nice touch!

These appear to be "real" shutters that should open (as shown) or close over the window to prevent broken glass in the case of bad storms such as large hail or hurricanes. I would check to make sure they close properly, meet in the middle and cover the whole window which will let you know if the shutters are warped or not. Yes, shutters that open and close "bend back" from the hinges to whatever is holding them open (the S shaped holder seen in your last photo). The appearance of warped shutters may be due to the angle of the photograph or more likely the fact that this appears to be an older home which probably is no longer completely plumb. It can be very difficult to fit shutters to older homes that have settled because the windows may no longer be perfectly plumb and straight. Although from all appearances in the photos these windows were recently replaced with modern Anderson windows which hopefully are plumb.

it might be the hold backs are too short, if you unlatch them are they straight?