yes.
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Yes.
Yes all inscribed angles in a circle have their vertex on the circumference of the circle. Central angles have their vertex at the center of the circle.
If you want to, you can always draw a circle around an isosceles trapezoid and the radius can be half the base of the trapezoid.
No, the circle is inscribed in the quadrilateral.
All geometric shapes can be inscribed in a circle, since the circle is bigger than the other geometric shape inscribed in it. (Obviously)