Similar shapes need to have the same number of sides, the same angles and the ratio of the sides needs to be the same. Rectangles are not always similar to each other because they can have different dimensions, which would break the "same ratio" rule.
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No. Two regular hexagons are always similar to each other, but two random hexagons are not necessarily similar.
Parallelogram
always
Only if 2 sides are parallel with each other, and the other two sides are also parallel with each other. All squares are rectangles. All rectangles are parallelograms. All parallelograms are 4 sided. But not all 4-sided are parallelograms, not all parallelograms are rectangles, and not all rectangles are squares.
They can b different sizes