I'd like to share a bit of what I know about this plant, and then if anyone has any info to share as well, I'd love to hear it! I love learning from the fine folks on OB!
The Platystele genus is responsible for some of the smallest orchids identified to date. Platystele Umbellata has the tiniest flowers I have bloomed so far. It blooms from winter until spring in intermediate to warm conditions and it seems to be fairly easy to bloom. It originates in Columbia and grows at elevations between 600 and 1600 meters.
I grow this plant mounted in my terrarium. The terrarium is misted daily in the mornings. This plant is set up so that it receives partial shade and gets about 8 hours of light from a CFL bulb. The moss pad around the roots of this plant gets watered with distilled water four or five times a week, depending the moss is just damp to the touch. I do not let it dry out completely. No fertilizer, just tap water once a week instead of distilled. This seems to be enough nutrients for it.
This little guy tried to hide his spikes from me. They were spiking behind the mount for another plant in the terrarium. I happened to notice the spike and managed to safely extract it and reposition the plant so that the spike is visible in the terrarium, which was quite a trick considering how tiny the spikes are on this guy. I was afraid I was going to snap one off if I touched it at all.
The flowers are not fully open and I can't find my macro lens, as soon as I do, I will upload a few more pics of more open flowers.