Hypoperfusion causes brain damage?

Yes. How did you measure the hypoperfusion, just low blood pressure, anemia, low heart rate, or you measured the cerebral blood flow.
Yes. Hypoperfusion means inadequate blood supply to areas of the brain. If it occurs for long enough, it will cause permanent damage.
Possibly. In general, hypoperfusion refers to decreased blood flow. Depending on the degree, location and and duration of hypoperfusion to the brain, yes, hypoperfusion can result in brain damage that may or may not be grossly observable (and/or modifiable) as it relates to the individual's day to day emotional/functional status.