The applet assumes that the particle is subject only to electric and magnetic forces. The gravitational force is not included.
The applet assumes that the electric and magnetic fields are uniform and non-zero between the capacitor plates and that both fields are zero everywhere else. In reality, a capacitor with plates of finite size will not produce an electric field that is exactly uniform between the plates and exactly zero everywhere else. Neither is it possible to produce a magnetic field like this. Thus, realistic fields will be different from those assumed here, but the errors introduced by assuming the given fields are slight. Moreover, all standard textbooks use the same kinds of idealized fields.