1. If your degree is on the INZ list of qualifications exempt from assessment, or if you get an IQA done by NZQA, then you can claim the points for a recognized qualification, even if not related to your work - probably 50 points for a bachelor's degree with honours. But you would still need to show that you are qualified in some way - by other qualifications, or by the amount of experience that ANZSCO says can substitute for a qualification - for any skilled job you are doing in NZ when you apply.
2. I don't think it's possible to give a brief and straightforward answer to this. You need to look here.
http://onlineservices.immigration.go...anual/6954.htm These are the detailed requirements to claiming each set of points available for the EOI. SM7.10 and SM7.15 give details of what is necessary to have any job in NZ recognized as being skilled work for the purposes of an application.