This link suggests that "suspension shock or strut replacement is between $876 and $925." I found similar details on other sites. Since I'm not familiar with this part, I am confused if that is saying $876 per strut and there are two struts, so I can expect to pay $1600+, or $876 is for a strut replacement and that means the whole part in the diagram that is going across the front of the car and that is one thing replaced. Should one expect higher costs if a strut has failed and it is poking through the wheel well and hitting the hood?
Those estimates are per strut. When you're replacing due to wear and tear, it's always good practice to do both sides on the same axle, but if the car was in an accident, you might do only one side.
If the strut is hitting the hood, something important (probably not just the strut) has failed. Take it to a garage, and expect some serious bills.
The struts are one at each corner of the car, so four in your picture. The strut usually comprises a strut housing, a damper, and a spring. Each of those components can be replaced separately. Tying the struts together is sometimes a lower "Subframe" which can span the front two struts or the rear struts. The first thing to fail is usually the dampers, resulting a floaty ride and usually lots of up and down movement when you go over undulations in the road. The next most common things to fail are the strut mounts at the top of the struts, if these start knocking or klunking then be sure to get them replaced as a failed strut mount will result in what you describe as the strut punching the hood, in the worst case a failed strut mount can destroy your wheel well which will result in body or frame damage.