A quadrilateral is any shape with four sides; angles can be acute or obtuse. A perfect square is the only quadrilateral with only right angles.
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A, a triangle
That would be a trapezoid. A trapezoid does not have to have two right angles it only needs to have two parallel sides. There is not a name for the exact quadrilateral you are looking for but the shape is still within the definition of a trapezoid.
A rectangle has four right angles. A square also has 4 right angles, but it is a only a square and not a rectangle if all of the sides are congruent.
Quadrilateral. No other special name. A kite could have 1 right angle - that's possible, but there is no special name for a quadrilateral with only 1 right angle.
A quadrilateral with 4 right angles can only be a rectangle or a square. A rectangle has only two lines of symmetry - the lines joining the midpoints of its opposite sides. So the answer cannot be a rectangle. A square has the same lines of symmetry as a rectangle, plus the two diagonals - 4 lines in all.