Computing an inverse Jacobian can be slow, but not that slow. It will run on a recent computer within a reasonable amount of time. It might not be real-time, but it won’t be far from it. Jacobian Transpose should be very fast, but not as accurate. Jacobian Pseudo-Inverse is another way to approximate the inverse; it is more accurate but is also slower.

“Each term in the Jacobian matrix represents how a change in the specified joint angle effects the spatial location of end effector.” In other words, E=<px,py,pz>. (not sure what D-H parameters are)

All questions are valid! Does this help?