Hi Reiner and welcome.
Many people have gone to NZ on a visitor's visa and looked for work when they were there but, of course, you mustn't let INZ know this is your intention. How long you can stay on a VV depends on where you are from. Those who come from the UK, for instance, can stay for up to 6 months but some other countries it is only 3 months. I'm not sure how long you would be able to stay, coming from your country, so it would be best to ask at the NZ Embassy there to give you an idea of how long you would have.
This is a guide to applying for a VV for NZ.
If you want to claim extra points for a job offer on your EOI, the job offer must relate to your qualification. You can't use just any job offer.
You could take your police certificate with you and I'm sure it would be easier, but be aware that they only last for a certain amount of time before you would need a new one. That would mean you would have to submit your EOI and ITA within that time.