Is the cross section of both a Trailing edge flap and elevator an aerofoil please or, like i've shwon in in image below? I tried to find a side view of an elevator and TE deflected to see this for myself, but couldnt find one
Many elevators have airfoil shapes.
The precise way you've drawn the flap is not physically possible. It is drawn as a shear of the trailing edge. That would involve deforming materials.
Instead, a control surface has a hinge and there is a rigid body rotation about a single axis. This usually means that the front of a control surface is an arc about the rotation axis.
On small general aviation aircraft, it is not uncommon for the elevator to be made out of welded metal tubing and covered with fabric. In this case, the elevator (and its control surface) will be flat plates with circular leading and trailing edges.
In general, to prevent control surface flutter, control surfaces need to be balanced (mass) around their hinge. In addition, it is often beneficial to add some sort of aerodynamic balance in front of the hinge. This is an extension to the surface that reduces the force required to deflect the surface.