Yes of course.
You must see the body as one whole unit by itself. Internal
forces within the body do not affect the motion. Only external
forces acting on the body do.
Strictly speaking, the person pushes downwards.
What you have just said were what we have explained. Perhaps u did
not understand the terms used. What we understand from your
definition of normal force is the reaction force from the ground,
which of course reduces to zero when you are not touching the
ground. It does not remain there. Because it is present for such a
short time, you may also call it an impulse. Mathematically, an
impulse is the multiplication of the force times the time of
application of force.
Yes, the resultant force is what causes the person to accelerate,
and it is due to the reaction force from the ground being greater
than the weight of the person.
If you are asking about the magnitude of the resultant force during
the whole course of the jumping motion, it cannot be answered
properly.
