A square has 4 lines of symmetry
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You would call the group of shapes which has at least one line of symmetry symmetrical shapes. Stars, circles, and rectangles are considered symmetrical shapes.
It all depends what types of shapes, but take for example a circle, it can have multiple lines of symmetry.
There are infinitely many such shapes. To start with, any regular will do.
None. A line of symmetry, if it exists, is infinitely long and so a third of the line cannot exist as a separate entity.
An order of symmetry is the number of times a line of symmetry can be drawn through a shape. For example, a square has four orders of symmetry: One up and down, one left and right, and two diagonal. A rectangle has an two orders of symmetry. A circle has an infinite number of orders of symmetry.