The “control strip” — the standard set of functions that have always been on the function keys – is somewhat persistent. It hangs out on the right side of the Touch bar in a minimized form. You’ll see that in the image of the Touch Bar samples that I included in the post, with volume and brightness controls showing persistently. There’s a little chevron on the left of that set of functions which can be expanded to show the other buttons on the control strip, including the iTunes controls. So nothing can be pinned as such, but all those controls are always just a tap away on the Touch Bar, and brightness and volume are always visible. You can set the Touch Bar to always show the full control strip if you want to, rather than app-specific functions. This is how this is explained in Apple’s reviewers’ guide for the Touch Bar:
The second thing you mentioned is not supported as far as I am aware. Other than the persistent control strip, which contains OS-level functions, there’s no way to show Touch Bar functions from an app while in a different one.