Is it possible to move the progress bar around? What if I wanted it to appear in the middle of the screen and not along the bottom? What if I wanted to shorten its length so that it only appears on half of the screen? Is it possible to edit the progress bar in this manner?
Look at the options under Project > Skin Editor.
You can position the playbar on any side of the screen and minimize it's size by not having it stretched. However, there is no option to make it a specific length.
Feel free to request that Adobe make enhancements to this area if you want. It's many years since there were any improvements to the playbar functionality.