An equilateral parallelogram is called a rhombus.
A parallelogram is equilateral when all its sides are the same length - that is, when it is a rhombus.
Yes, but only if it is a square. A square is an equiangular rhombus, and a rhombus is an equilateral parallelogram.
A rhombus, by definition, must be equilateral. Therefore, an isosceles rhombus cannot exist and so it cannot be a parallelogram.
A trapezium has only one pair of parallel sides. A parallelogram has two pair of parallel sides. A rhombus is an equilateral parallelogram - that is, a parallelogram with equal sides.
No, a parallelogram is not a trapezoid.