I met a young healthy lady who got paralyzed after surgery, what causes this? Too much anesthesia medicine? Will be undergoing one myself. Please help.

Not enough info. Need to know what kind of surgery, what the anesthesia was (general vs a block such as spinal or epidural). Also need to know what kind of medical problems the young healthy lady may have had ---although she says she is healthy or looks like she is, she may have something that can can go on to cause paralysis.
Anesthesia. Anesthesia is very safe, unclear what surgery your accuantant had, but the cause most likely related to underlining disease . You did not provide full history. Talk to your anesthesiologist before surgery, he will help you with your questions and anxiety.