It may be local New Zealand idiom, but 'no fear' here means (or meant) 'no way', i.e. it is a refusal or denial. So - in terms of an imperative as a replacement for 'don't be afraid', then no, neither of those would be used like that.

no fear: there is no fear in doing something means no need of worry Don't be afraid to raise your hand if you don't understand something.

Not that I know of, I never hear "no fear" or "fear not" colloquially. But I live in the US, not sure about British English.