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A quadrilateral in which each side is parallel to its opposite side is called a Parallelogram.
There are special types of Parallelograms, like Rhombi, Rectangles and Squares.
The opposite sides of Parallelograms and Rectangles are equal but their adjacent sides are not necessarily equal, plus, their diagonals is their sides are unequal do not bisect at right angles.
Now, Rhombi and Squares have all sides equal and their diagonals intersect at right angles.
The angles of Rectangles and Squares are all 90 degrees and have diagonals of equal length.
The angles of Parallelograms and Rhombi are not 90 degrees, but their adjacent angles add up to 180 degrees. Their diagonals are of unequal length.
With these given facts,
The quadrilateral you have described is, surely and without a doubt, a Parallelogram.
The quadrilateral could have become a Rectangle if the question had further specified that either its diagonals were equal or all its angles were 90 degrees
that is the answer for 1st problem