Does everybody have to do the medical check?
You do not need a medical check for your registration at all.

Don't mix up immigration with registration - 2 completely different things.

I don't know how long the minimum period is, only, that you have to sign a declaration that you intend to practise in NZ. The APC in NZ costs $255,- - you might as well want to work for a while to make the APC worthwhile...

Good luck!!!