Yes, if two triangles have two congruent angles and two congruent sides then the triangles are guaranteed to be congruent. They only need two angles and one side congruent or two sides and one angle in order to be congruent.
opposite or vertical angles
A parallelogram cannot have only two congruent sides, nor only two congruent angles.
YES, if they have the same radius.
Are congruent circles.
a cylinder has two faces that are circles
Congruent circles, maybe...
They are arcs of congruent circles.
The same radius.
Only if they belong to congruent circles.
same circle or congruent circles
No, but they can be. They would be similar.