Your mouse must be over the 3D Viewport, you must be in Object or Sculpt Mode, and the active object must be a mesh. If several objects are selected and none is an active mesh, select just the one you want to pose and press U again. Also check that no other addon is using U in the 3D View keymap.

Transpose Classic writes directly to the base mesh coordinates. With shape keys present, those edits would conflict with the key data. Apply your shape keys (or remove them) and the tool will start normally.

Not while the Multires modifier is visible in the viewport. Disable its viewport visibility to work on the base level mesh, or apply the modifier if you are done with multi-resolution sculpting.

The tool only protects masked vertices. If nothing is masked, everything moves. Paint a mask over the areas that should stay still in Sculpt Mode, then start the tool. You can invert the mask with Ctrl + I if you masked the wrong side.

Soften the edge of your mask. Partially masked vertices move partly, so a blurred mask edge gives a smooth falloff. Use Smooth Mask from the Mask menu, or paint the edge with a lower strength mask brush.

Blender's tools also respect the mask, but you set the pivot separately. With Transpose Classic, you draw the line on the surface and the pivot and axis come with it. Rotating from an end handle pivots around the opposite end, which is how joints behave. That makes posing limbs and fingers much faster.