> what the last one is supposed to do.
It's indicating an iOS device being locally, e.g. for administration, backup, file transfer and the like.
> Are the things above that row buttons? Why don't they look like them then?
Haha yeah. That's modern Apple for you!
> what does fast forward and rewind do?
They sort of behave the way ff and fr does on a remote. Click/press fast and you skip to the next/previous song/chapter or equivalent. Hold down and you scrub at something like 4x speed.
> Is that slider a progress bar or volume slider?
A volume slider.
> Where do I click and drag to move the window? If it's in that top row, why are there things cluttering up the title bar? How much space do I have left to move the window?
I ask myself the same thing every day and have the same problem with many many apps, also in Windows. For example Firefox has the same design problem where its buttons have nor border and therefore have no clear place where draggable top space is and button is.
> I assume the coloured things are the window management controls.
Yes, these have remained mostly unchanged for over 20 years, they have gotten a bit flatter and lost some subtle small iconography.
> Does clicking the red one close the window and keep the music going
At least this part works well and in a predictable fashion. It consistently follows Apple's Human Interface Guidelines since well over 30 years: Closing a window or document of a Mac OS application should not quit the application. (there are some exceptions, but that is the default behaviour).