Yes
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A trapezoid.
Yes, easily.
Yes, they are.
Because Corresponding Parts of Congruent Triangles, there are five ways to prove that two triangles are congruent. Show that all sides are congruent. (SSS) Show that two sides and their common angle are congruent. (SAS) Show that two angles and their common side are congruent. (ASA) Show that two angles and one of the non common sides are congruent. (AAS) Show that the hypotenuse and one leg of a right triangle are congruent. (HL)
No, because the third-angle theorem requires that you know two angles of each of the triangles. Assuming ASS, you only know one angle. In fact, two triangles may have the same ASS and not be congruent. See if you can make two non-congruent triangles with Angle 60 deg, Side 10, and Side 9.