A Square is a Rhombus as a Square has all the properties that a Rhombus has, two pairs of equal sides that are parallel to each other and that all sides are of equal length . However, all the angles in a Square are right angles (90 degrees). While in a Rhombus, the angles in it are not right angles (90 degrees). Thus, it can be said that a Square is a Rhombus but a Rhombus is not a Square.
All of the statements are correct. Squares and Parallelograms are quadrilaterals as they both have 4 sides each. Opposite sides of Squares and a Parallelograms are parallel as the two lines never meet even if they go on forever.
No, I do not agree with this statement. Parallelograms do not have 4 equal sides, which is a property of a square. This alone makes it impossible for all Parallelograms to be a square. Unless it is a Parallelogram which has 4 equal sides, in which the shape would be called a Rhombus instead of a Parallelogram.