Yes
sometimes
Sometimes they are.
Two squares are always similar. Similar figures have the same shape but can differ in size, and since all squares have equal angles (90 degrees) and their corresponding sides are in proportion (all sides are equal), any two squares meet the criteria for similarity. Thus, regardless of their size, any two squares will always be similar.
sometimes
Never
sometimes
Sometimes they are.
Parallelograms are squares is sometimes true. Squares are parallelograms is always true. Rhomboids are parallelograms is also always true. So not all parallelograms are squares but some are.
sometimes
Sometimes similar but it depends
sometimes
Never
Sometimes.
If they are congruent they must be similar.
Perfect squares will never be irrational numbers. A perfect square is the result of multiplying an integer by itself, which always yields a rational number. Since the square root of a perfect square is an integer, perfect squares are always rational. Thus, they cannot be irrational.
Some parallelograms are squares - the ones which are equiangular (have equal angles) and are equilateral (have equal side lengths). All squares are parallelograms, but only some parallelograms are squares.
If they have the same nuber of sides (angles) then always. If not then never. So, overall, I suppose the answer is sometimes - depending on the number of sides.