Does Inkscape have a tool like GIMP's "shear" tool? One for skewing the perspective of a thing?
Unlike GIMP, there's no actual tool in the toolbox for skewing or perspective. Probably best not to try to compare GIMP and Inkscape as they are both very different kinds of software.
However, a skew can be achieved directly on an object by clicking on it twice with the Select Tool S to bring up the rotation and skew handles, then click and drag on the midpoint of an edge to skew. Or alternatively by using the Skew tab in the Transform panel for numerical input.
The Transform panel can be opened using Object > Transform or Shift+Ctrl+M
Perspective distortions can be achieved using the Perspective/Envelope Live Path Effect. After selecting an object with the Select Tool S and applying the Path Effect, switch to the Nodes Tool N and you can click and drag the control points. Note that this doesn't work on editable text objects; they must be converted to paths first.
The Live Path Effects panel can be opened using Path > Path Effects or Ctrl+&
Note: If you want to apply a Path Effect to a path, you can use Path > Object to Path.