You have to stretch a string a little to sharp it, and this raises it's pitch, irrespective of the amount you shorten it. A relatively slack string undergoes more of a pitch change than a tighter one, so you have to change the location of the sharping lever to compensate.
Acoustic impedance is the tendency of an object to resist being driven at a certain frequency.
Technically, it is the ratio of force to velocity at a given frequency, place, and time. It took me a while to get the handle on this myself. The easiest way to visualize it is to think of a thin stick of wood with a weight on the end that has been clamped to the edge of the table, such that the weight is swinging in the air, and see what kind of work you have to do to swing it up and down. If you try to move the weight up and down very slowly you will have to push against the stiffness of the stick all the time, but less when it is in the middle of it's swing than when it is farther out, of course. On the other hand, you won't have to put much energy into moving the weight, because at such low speeds it won't have much momentum.