Yes. Two angles are compliments ("complimentary angles") if they add up to 90 degrees. E.g. 40 degrees and 50 degrees are compliments to one another. A 45 degree angle and another 45 degree angle are both complimentary and congruent (same angle).
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Yes providing that the two equal angles are acute angles
No. It is not possible in Euclidean planar geometry (if you don't know what that means, it means "the only kind of geometry you've ever heard of") for a triangle to have two obtuse angles.
No not ever because the 3 interior angles of any triangle add up to 180 degrees and so an obtuse triangle will have 1 obtuse and 2 acute angles.
Verticle angles.
if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.