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Not necessarily. Rectangles are quadrilaterals and have no acute angles.
Yes. Rectangles have four right angles.
Any polygon can contain acute interior angles.
Any shape with 4 acute angles must have more than 4 sides. Any shape with more than 4 sides can have 4 acute angles (but doesn't have to).
Just about any shape that isn't a circle can have two or more acute angles. But with some of them, you need to make them have acute angles.