“Small 2-inch approximately terracotta-looking pot with something burnt in it. Found it at work.”
"This is a Diya. Yesterday was Diwali, the Hindu Festival of Lights. They light this Diya with this wick (of cotton) dipped in mustard oil/ghee and it lights very beautifully."
More likely an adhesive spreader for plastic tile, or to rough groove fresh concrete for traction.
#14 could be for keeping various plants on display. My grandmother had something similar for that, only with a few less shelves.