Question

Did I put correct answers?

Answer 1

Yes, you have the right answer for part 1.

But for the second part it should be A.  Because if it is a square, it has to be both a rectangle and a rhombus, that is the only way to prove it. 

We know it is a rhombus because we are given a right angle. And rhombus' diagonals are the perpendicular bisector of each other. we know the diagonals are both perpendicular bisectors because the segments divided are congruent, and it created a right angle.  Therefore, it is a rhombus. 

We know it is a rectangle because we know rectangles' diagonals are congruent.  We can see all four segments are congruent, so "if congruent segments are added to congruent segments, then the sum is congruent". So the diagonals are congruent, showing it is also a rectangle.
 
So when a figure is both a rectangle and a rhombus, it is a square.

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