No, you can not calculate an area if you know just the perimeter. For example, rectangle with sides of 10 and 20 would have a perimeter of 60 and an area of 200, but a square of sides 15 would have a perimeter of 60 and an area of 225. You need to know more details about the shape than just the perimeter.
It is impossible
Then they both will have the same perimeter
You need to know perimeter when you're fencing the yard. You need to know area when you're mowing it, seeding it, fertilizing it, buying it, or selling it.
You cannot. For a given area, an equilateral triangle will have the smallest perimeter but that perimeter can be increased - without limit - without increasing the area.
You square-root the area
The area of a square is equal to twice the square's perimeter.
When you are buying a house you will want to know how much you land you have (area) and you will also want know how much fencing you need for you garden (perimeter).
Not exactly. If I know the side lengths, I can still find the perimeter
You can't. The perimeter doesn't tell the area. There are an infinite number of shapes with different dimensions and different areas that all have the same perimeter.
Divide the perimeter by 4 and then square the result to find the area of the square.