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yes concave is like a cave
A concave is not a shape. It is a characteristic of one. It is like asking how many parallel lines a small has.
A concave mirror bulges away from the incident light. The image of an object depends on where exactly the object is placed - relative the to focal length of the mirror. See the attached link for more details.
No
A geometric star shape is concave. A star that is in the sky is convex.