There is no special name for such a shape.
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It could be a kite, an arrowhead or an irregular quadrilateral with a right angle - which has no specific name.
A general quadrilateral or a kite.
Not possible... The internal angles of a quadrilateral always total 360. If you MUST have an angle of 90 degrees - the remaining angles must total 270. At least one of the remaining angles will always be obtuse.
A Right Triangle or sometimes called a Right-angled Triangle has one angle = 90 degrees
A quadrilateral is inscribed in a circle it means all the vertices of quadrilateral are touching the circle. therefore it is a cyclic quadrilateral and sum of the opposite angles in cyclic quadrilateral is supplementary. suppose if one angle is A then another will be 180 degree - angle A.