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Tangent plane "is the floor". I never heard that the touching point has a specific name.
A trapezoid is never a parallelogram. The definition of a parallelogram is a four sided figure with 2 pairs of parallel sides and a trapezoid only has 1 pair of parallel sides.
A trapezoid is a four-sided figure with only one pair of parallel sides. A square will always have two pairs of parallel sides.
Not all trapezoids are kites. A trapezoid is a 4-sided figure with a pair of parallel sides, so any item, not just kites, can manifest this shape.
The answer depends on which definition of trapezoid (or trapezium, outside of North America) is used.Some mathematicians define a trapezoid as any four-sided figure with at least one pair of parallel sides. Using that definition, a rhombus is a special type of trapezoid because a rhombus is a figure with two sets of parallel sides.Others are more strict, using the name trapezoid only for four-sided figures with exactly one pair of parallel sides. By this definition a rhombus is not a trapezoid.