That is correct, when you flip the beam, the shear changes sign but the moment does not. This is the convention used. Always draw shear and moment diagrams from left to right. In this manner, the area under the shear diagram between 2 points will be equal to the change in moment between those 2 points. And the slope of the moment diagram at any point will be equal to the shear at that point. Stick with the convention.
Edit: regardless of convention, some of the directions of the shears and moments in your free body diagrams are shown in the wrong direction. The directions on a cut section are the same no matter from what direction you look at the beam.