Not required.
A square is a rhombus, but so are many kites. The rule for a rhombus is that all four sides are equal length. The opposite angles on a rhombus are always equivalent, which I think comes from the hinge theorem, but I haven't looked into that for a while.
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No. A rhombus is a parallelogram with all equal sides. A parallelogram with all equal angles is a rectangle (which might also be a rhombus and a square).
A rhombus is a special case of a parallelogram, where all sides are equal length. A rhombus and a parallelogram have the opposite vertices are equal angles, but adjacent angles are not necessarily equal.
Not unless all angles are also equal. A rhombus is a parallelogram with all sides equal. A rectangle is a parallelogram with all angles equal. A square is a rhombus with all angles equal which is a parallelogram with all sides equal and all angles equal.
Not necessarily.The sides of a rhombus are all equal.The angles are all equal only if it's a square; then they're all right angles.If it's not a square, then the rhombus has two pairs of equal angles.
A rhombus has two equal opposite acute angles and two equal opposite obtuse angles with all four angles adding up to 360 degrees.