Take the following situation, ignoring friction. I apply a force to one side of the square object. Does it begin to both rotate AND move linearly in the direction of the Force?
If so, does the force contribute independently to rotation and linear movement, or does it depend on how far off center the force is?
Take the following situation, ignoring friction. I apply a force to one side of the square object. Does it begin to both rotate AND move linearly in the direction of the Force?
Yes and yes.
If so, does the force contribute independently to rotation and linear movement, or does it depend on how far off center the force is?
It does contribute independently to rotation and linear movement. But the degree of rotation is dependent on how far off center the force is, because torque about the COM is the product of the force and the perpendicular distance from the COM.
A force can be moved any amount parallel to its line of action, provided one includes couple to account for its moment $M$ or torque about the COM, constituting a force couple system. A couple is two equal and opposite parallel forces.
The diagram below at the right is a force couple system equivalent to the force on the left. The force has been moved to the COM and a couple added to represent to moment (rotation) about the COM due to the offset force. Note that the couple involves no net force, only a pure moment or torque. The net force $F$ acts through the COM.
Hope it helps.
