In order to make a card move forward, a horse must pull harder on the cart than the cart pulls on the horse? true or false?

That's false.  Remember:  The action and the reaction are always equal.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards