On black sticks that have a warty surface, perhaps Sycamore, Elm, or Hackberry? Those are the most common tree species in the immediate area that seem to be possible candidates for these wood remnants that this species of Sarcoscypha seem to feed exclusively upon.
ADDENDUM: Identification to species supported by microscopy with photos, generously provided by and credited to Adam Boring. @pipsissewa
Growing on twigs under Hickory, Hickories are diverse species in the immediate area, shagbark, pignut, and either mockernut or butternut.
Very small, no larger than a dime, on top of soil under leaf litter
Small, stalkless, red cups growing directly on clay mixed bare place in soil and leaf litter. Specimens consistently smaller than a dime. Glabrous, no hairs.
Appears to have fairy pins (Phaeocalicium polyporaeum) growing on them!
Not sure about this one. Would love to know.