I wouldn't tell you definitely that it's wrong, but it doesn't sound quite like something we would say in English. "On the left-hand side" or "on the left side" is fine.
Or even "on the left". "On the left hand" sounds like she is living on the thing attached to someone's left wrist.
No, I wouldn't go that far. "On the left hand" does mean what it's intended to mean, it just doesn't sound like quite the right way to say it.
Maybe it's just me, but that's what I'd think if I heard it. It's entirely possible that I'm just weird, though. :-)
В одному з завдань було - "моя школа праворуч - my school to the right", а в цьому завданні те саме, але "to the left" - неправильно! не розумію чому!!!!
It depends on the context. If we mean the direction of motion we use "to". You go to the right. If we mean the location we use "on". You stand on the right.