Is this sentence grammatically correct?
It is fine - you could say 'there' instead of 'in that place' unless you prefer it to sound a bit more dramatic
the last three words are unnecessary, but it's still OK to me
Yes it's fine. No alteration necessary.
Remove "in that place".
It is grammatically correct. As a matter of style most of us would remove 'in that place', but that's style, not correctness - they are two separate issues.