For question 1, I don't think there is any theorem/postulate that can help prove the congruency of the two triangles since there is no SSA postulate/theorem. For question 2, I don't think there is a theorem/postulate that can help to prove the congruency of the two triangles, since there is no AAA postulate/theorem. For the last question, I think the answer is the Hypotenuse-Leg (HL) postulate, since you know that the hypotenuse and one of the legs are congruent to each other. And in proving right triangles congruent, you only need to know two congruent angles/sides, since you know that all right angles are equal to each other
Hope this helps! ^-^