Like many here, I have not seen the Broadway play, but it seems that when Henry became 001 with Dr. Brenner, he spent a short time in Dimension X looking for Dr. Brenner's father and that is when he encountered the "first shadow" (which I think we are led to believe is the Mind Flayer). In this encounter, Henry was physically changed, including his blood. Once he returned to "our world", he developed these powers. Dr. Brenner's experiments then shifted to the other kids who were literally injected with 001's blood. Conversely, the Mind Flayer already existed long before it's encounter with Henry but it was Henry, once banished to X by Eleven, that gave the shadow its shape, which we see in the later seasons. All the time that Henry spent in X eventually led him to become Vecna.
The Upside Down is a decaying version of Hawkins that is frozen in Nov 6, 1983. How Vecna gained access to here, that I haven't quite figured out?