distance calculation of Rotation and Translation matrices of 2 objects on the same plane

Answer to 2): If translation is the vector resulting of subtracting point2's position to point1's position then Euclidean distance follows the formula linked here.

Then you just need to compute sqrt(x^2 + y^2 + z^2) as (x,y,z) of translation vector(between 1 and 2) as it is already the difference between the two points coordinates.

That means you have to compute the euclidean norm of the translation vector.

If you have 2 translation vectors (one for each point) then just subtract them, and calculate the euclidean distance of the resulting vector.

1) Yes, it is. If 2 objects are refered to same coordinate system, and them have the same plane (the vector view is the same), at force, they have the same Rotation matrix. You can learn how a rotation matrix is build HERE. It is very userful if you don't know how are build. It has an example very good. 2) You can use the Euclidean distance using the same point (the center of reference for each object). It is the same of traslation.

Remember: 1º do all rotations, and then traslation. If you traslate 1º, you will do it wrong.

Hope it help!