1) Jacobian is nothing more than linearizing your dynamic model and measurement model at a particular point. So once you write your models, it will be easy to construct the Jacobians.
2) This depends on what assumptions you want to use. If you are tracking a moving object, there are various models, e.g., constant turn rate and acceleration, constant turn rate and velocity, constant acceleration...
so in your case, if you assume constant velocity (r_dot does not change during the time step), r(k+1) = r(k)+r_dot(k)*dt
3) There are many academic papers on this topic. Search in google scholar for 'extended kalman filter motion tracking' and take a look. They generally give you the equations as well. Pick one that is easy to understand for you.
4) Both are equally viable. It will only change how your equation looks, and the pysical interpretation of the tunable parameters of the Kalman filter, noise levels etc.
