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A square, a regular hexagon, regular pentagon and all regular polygonal shapes
They can have some (or all) equal angles. A rectangle, for example, has all four angles equal but, because its sides are not the same measure, it is not a regular shape.
There is no such shape. A 2d shape with 5 sides and all equal angles must be a regular pentagon (or a 5-pointed star if you stretch the definition of "all angles"). And a regular pentagon - or star - has 5 lines of symmetry.
A shape where all sides are equal lengths, and all angles are equal. Also all external angles add up to 360o.
An octagon can be an irregular shape, but a regular octagon has all sides and angles equal.