What is a down arrow icon called?
Caret (or downward-facing arrow)
What symbol indicates no change?
a thin dash (e.g. -), a thick dash (e.g.━), a (no change) label following the value. nothing at all.
Which way do accordion arrows go?
Arrow Conventions
Trees have used right-pointing arrows for closed and down-pointing arrows for opened, which, as FreshCode mentions in his answer, has been generalized to expanders.