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The maximum area that you can enclose with 3000 feet of fencing would be a circle of radius 477.46 feet. This circle would have an area of 716197.2 square feet which is 16.442 acres. The minimum area that you can enclose is infinitesimally small - go for a very, very long and very, very narrow area.
Anything up to 154.06 sq feet. The above value is attained by a circular garden. A quadrilateral garden has a maximum area of 121 sq feet but the minimum is as close to zero as you wish.
If the acreage is a square, you'll need 6,467 feet of fencing to enclose the area.
Depends on the shape of the area (see the answer to the same question relating to 2 acres). If the area was an infinitely thin strip, the length of fencing would be infinite. For a circular area, the least amount of fencing would be needed.