A defining attribute is that it has two pairs of parallel sides. There are lots of other attributes which can be derived from this.
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No.
A rhombus is a special kind of parallelogram (all its sides are of the same length). So things that are true of a parallelogram are true of a rhombus. It has two sets of parallel sides, its adjacent angles are supplementary. Other attributes, that follow from these also apply.
1. All 4 sides same length 2. Is a parallelogram 3. Opposite angles are equal 4. Can be a square if all angles are 90°
Yes all rectangles are parallelogram but all parallelogram cannot be rectangles.
A parallelogram where all sides are equal is a square.