No quadrilateral with 2 internal right angles can be anything other than a square or rectangle. The shape described in the question does not exist.
Improved Answer:-
It could be a trapezoid with two right angles, an acute angle and an obtuse angle.
It is a convex quadrilateral, as the remaining angles could be any two angles with a sum of 180 degrees.
Both a 'kite' shape and a right-angled trapezium can have exactly two right angles
Yes, a quadrilateral can have two obtuse angles. In fact, a quadrilateral can have up to four angles, and as long as the sum of all four angles equals 360 degrees, it can accommodate two obtuse angles. The remaining angles would need to be acute or right angles to satisfy this condition.
a trapezoid
It's a square.
It is a convex quadrilateral, as the remaining angles could be any two angles with a sum of 180 degrees.
Any quadrilateral in which at least one (and therefore at least two) angles are not right angles is not a rectangle. The majority of these do not have a specific name.
Both a 'kite' shape and a right-angled trapezium can have exactly two right angles
It is called a Rhombus.
A rectangle.
A kite can have exactly two right angles.
A 4 sided polygon is called a quadrilateral. Depending on where the two right angles are, would put the quadrilateral into different subsets. For example if the two right angles are on adjacent corners (and the other 2 angles are not right angles), then it is a trapezoid. If the 2 right angles are in opposite corners, and the other 2 angles are not right angles then it would be a kite-shaped quadrilateral.
A, a triangle
A Rhombus
trapeziod
none
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.