(1) Currently no, local numbers can not be ported to mobile, however Vodafone petitioned the ComCom to seek clarification on what is defined as a local number and what is mobile. Have a look at http://www.tcf.org.nz/library/a5458296-61ba-4474-b799-2eaa9bf01168.cmr page 32. This is also very good plain English what is LMNP.
(2) Its up to customers to check, the Telco knows since it has it in its DB, this can be problematic for customer that say has free calling on Voda to Voda calls but they don’t know their friend has moved to TCNZ with 021. As below each Telco has advised their customers on this.
(3) Similar for local and national except that the customer pays no matter if they are business and res it works the same apart from no local calling charge.
(4) In simple yes, the new entrant would need to comply to the comcom rules and negotiate with local telcos depending on what they wish to do.
tama: As for the initial question, yes IPMS is a live database and each ISP will be running a daily check (should be more than once a day, but it depends on each ISP preferences really) to make sure their copy of the IPMS database is up to date. Thus it will make sure that each ISP knows where to route a call to.