Let's say an object hits a wall. When the object is reflected does the direction of the reaction force caused on the wall look like the red arrow? Does that direction depend on how "strong" object is reflected?
Since you are saying an object i am considering it to be a rigid particle.Now,since the particle strikes the surface as in your figure.it gives a downward force on the surface and hence the reaction is obviously upward. As you must be knowing normal reaction is perpendicular to the surface.So break the black arrow in componentsi.e you can imagine the ball to be coming rightwards along Y and towards the surface by X.For Y no reaction force and the reaction N is due to the component X and hence directed upwards.
Regarding your second question-magnitude of N depends on a number of factors-not only on the speed but also the rigidity of the wall,ball.What you can tell by the change of speed is the impulse given $\int \vec f dt=m(\vec v_2-\vec v_1)$.As you can see by the cannot in velocity,you cannot predict the strength ofthe reaction as time comes as a product which in turn depend on their material.