Not necessarily.
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yes.
No. All rhombi (rhombuses) are parallelograms but all parallelograms are not rhombi.
1 hexagon = 3 rhombi so 3 hexagon = 9 rhombi
All squares are a special type of rhombi. The special feature is that all angles of squares are equal.
Strictly speaking, no, because a semi-regular tessellation must be based on regular polygons and rhombi are not regular polygons. However, octagons and rhombi can be used to make a non-regular tessellation.