1st question is ambiguous. You must define the point around which it is rotated. And then you have to say whether you mean a rotation degree less than 360 (because everything has a rotation symmetry of 360 at least). If the point of rotation is at the intersection of the diagonals then yes.

Yes. Example: lengths 2, 0.5 and 1,1: areas: 1,1; perimeters 5, 4.
Yes. Example: lengths 1,1 and 1.5,0.5: perimeters 4,4; areas: 1, 0.75