Cardiac cycle and atrial contraction
While blood is flowing into the ventricle, it can never be at a higher pressure than where blood is flowing from: if it was, the flow would be going in the other direction. Flow is always from higher to lower pressure, if there is no pressure difference there is no flow.

Before atrial contraction, the ventricle can have no more pressure than the uncontracted atrium, which in turn can have no more pressure than the veins (vena cava or pulmonary depending on which side of the heart we are talking about). When the atrium contracts, it increases the pressure in the atrium, which causes a flow of blood into the ventricle. Whenever a fluid flows, there is a pressure drop that depends on the resistance (very much like voltage in an electrical circuit). However, the AV valve is fairly big and open, so there is little pressure drop from the atrium to ventricle.


  The pressure is equilibrated between two sides of an open valve.


...is mostly true if the valve is large enough. There is still some pressure drop, though: if there wasn't, there wouldn't be flow.

There is no need for the ventricle to be at maximum capacity for pressure to increase. Imagine if you squeeze one side of a balloon: the pressure in the balloon increases, which you can tell because the balloon stretches and expands in the areas you are not squeezing; it need not be at the maximum capacity of the balloon for this to happen. Same for the heart.

As far as the higher pressure in the aorta, I this diagram is slightly exaggerating where the pressure difference starts, but as the ventricle relaxes there is a brief time where you get a small backward flow because the relaxing ventricle ends up having less pressure than the proximal aorta. This pressure drop is what closes the aortic valve (or the pulmonary valve, same process).