Yes, two angles can be both supplementary and congruent
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No, a pair of angles that are supplementary will always have a sum of 180 degrees, while a pair of angles that are congruent will have the same measure. Therefore, it is not possible for a pair of angles to be both supplementary and congruent.
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Angles that are congruent and supplementary must be right angles.
No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
congruent
All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.